I'll give a brief idea of some of the factors in play on a Tellarite ship. Tellarites found human rooms cold, and that demonstrates that they have a higher body temperature than other humanoids. This would indicate that temperatures on Tellarite ships would be warmer.
Tellarites are shorter than other humanoids. Gral was played by Lee Arenberg, who is 5'4''. I cannot find data on Gav from "Journey to Babel", but he appears to be somewhere between 5'6'' and 5'8''. He is dwarfed by Mark Lenard as Sarek, at 6'0''. His Tellarite compatriot appears to be tall for a Tellarite, perhaps closer to Shatner's height of 5'10''. This presents a canon problem, because we can either go with the idea of Tellarites being quite shorter as shown on ENT, or somewhat shorter as shown by the few on TOS. I would go with the idea of Tellarites being rather shorter than humans on average (5'4''), with the tallest being only as tall as an average human (5'10'') and most falling beneath that (5'8'').
What we can infer from this is that Tellarite ships would be internally shorter compared to those of other humanoids. Doors could be shorter, as well as ceilings and work stations. This is for the very simple reason that they do not need them to be taller, and having them be taller would present an inconvenience. This would also have the benefit of more space that could be freed for other purposes. Collectively, the amount of space that is freed could be significant, and dedicated to storage, living space, computer space, scientific equipment, and so forth. Tellarites are shorter, but just as wide as any other humanoid, giving them a portly appearance. Therefore, I think we can assume their ships could be shorter in terms of deck levels, but as wide as any other ship.
In terms of recreation facilities, we know limited things about the Tellarites, but can infer based on what we know. They take mud baths, so that may be an option. If that is something they do as a normal grooming ritual rather than simply for luxury, then we could find a mud bath in any Tellarite bathroom. We also know they enjoy debating, so their other recreational facilities could be dedicated forums for argument and debate. This could take the form of a normal Rec Room, with debate while they eat or modifications to that room to allow for such a thing. Or it could be a room dedicated purely to that.
In terms of how this would affect a Constitution class starship, I think it is based on how much we could assume a Constitution class would/could be modified. There are things that are easy enough to modify. These are temperature and recreational facilities. The Tellarites need a debate stage or a mud room more than a bowling alley. In terms of height issues, that would be a more significant modification. It would free up so much space, and it is an interesting idea, but it would take great changes to the design during the building process which Starfleet may not go in for. However, work stations may need to be tailored to Tellarite height and physiology. Otherwise, they may find it awkward.
I have left out one issue, which is the Tellarite hand. The canon is awkward on this. In TOS, they have two thick fingers and a thumb. This makes them more resemble pigs. In other Star Trek media, they have five normal fingers. If we assume two fat fingers and a thumb, the work stations should ideally be modified. They could handle fewer buttons at one time, would have limited dexterity, and would react slower per the number of buttons they would have to press. And reaction time, when there is a space amoeba about to eat you, is important. So buttons may need to be streamlined to be more simplistic, or for what thing they need to do being easily completed via just a few buttons but with more detailed work still accessible.
Tellarites are shorter than other humanoids. Gral was played by Lee Arenberg, who is 5'4''. I cannot find data on Gav from "Journey to Babel", but he appears to be somewhere between 5'6'' and 5'8''. He is dwarfed by Mark Lenard as Sarek, at 6'0''. His Tellarite compatriot appears to be tall for a Tellarite, perhaps closer to Shatner's height of 5'10''. This presents a canon problem, because we can either go with the idea of Tellarites being quite shorter as shown on ENT, or somewhat shorter as shown by the few on TOS. I would go with the idea of Tellarites being rather shorter than humans on average (5'4''), with the tallest being only as tall as an average human (5'10'') and most falling beneath that (5'8'').
What we can infer from this is that Tellarite ships would be internally shorter compared to those of other humanoids. Doors could be shorter, as well as ceilings and work stations. This is for the very simple reason that they do not need them to be taller, and having them be taller would present an inconvenience. This would also have the benefit of more space that could be freed for other purposes. Collectively, the amount of space that is freed could be significant, and dedicated to storage, living space, computer space, scientific equipment, and so forth. Tellarites are shorter, but just as wide as any other humanoid, giving them a portly appearance. Therefore, I think we can assume their ships could be shorter in terms of deck levels, but as wide as any other ship.
In terms of recreation facilities, we know limited things about the Tellarites, but can infer based on what we know. They take mud baths, so that may be an option. If that is something they do as a normal grooming ritual rather than simply for luxury, then we could find a mud bath in any Tellarite bathroom. We also know they enjoy debating, so their other recreational facilities could be dedicated forums for argument and debate. This could take the form of a normal Rec Room, with debate while they eat or modifications to that room to allow for such a thing. Or it could be a room dedicated purely to that.
In terms of how this would affect a Constitution class starship, I think it is based on how much we could assume a Constitution class would/could be modified. There are things that are easy enough to modify. These are temperature and recreational facilities. The Tellarites need a debate stage or a mud room more than a bowling alley. In terms of height issues, that would be a more significant modification. It would free up so much space, and it is an interesting idea, but it would take great changes to the design during the building process which Starfleet may not go in for. However, work stations may need to be tailored to Tellarite height and physiology. Otherwise, they may find it awkward.
I have left out one issue, which is the Tellarite hand. The canon is awkward on this. In TOS, they have two thick fingers and a thumb. This makes them more resemble pigs. In other Star Trek media, they have five normal fingers. If we assume two fat fingers and a thumb, the work stations should ideally be modified. They could handle fewer buttons at one time, would have limited dexterity, and would react slower per the number of buttons they would have to press. And reaction time, when there is a space amoeba about to eat you, is important. So buttons may need to be streamlined to be more simplistic, or for what thing they need to do being easily completed via just a few buttons but with more detailed work still accessible.
