Registries are more reliable than you're giving them credit for, but that's another topic.
They're usually a good indicator, but there are all sorts of outliers that are never treated as if it's anything out of the ordinary.
I'm not sure why the Brattain wouldn't have had a suffix after the registry if it was using the same registry as an older Brattain. Besides, most of the time newer ships with the same names as older ships have completely different registry numbers. Plus, the dedication plaque does not say 'second starship to bear the name' or similar info. So for all we know, this Brattain was the first one.
Prior to DSC, we only rarely ever saw a reused ship name/registry get a suffix other than Enterprise. Usually yes, the name is reused with a different registry. You have the Defiant, which... is destroyed and then they just relabel Sao Paolo as if nothing happened.
Starfleet doesn't seem to have a completely standardized way of doing this.
Every Miranda class ship in TNG and DS9 (granted there were only three) had been upgraded internally from the TMP movie era. Even the oldest ship (based on its NCC-1837 registry) which had been relegated to supply ship duty with minimal crew had its bridge updated (they used the Ent-D battle bridge.) Maybe you're thinking of the Constellation class Stargazer, which used the TMP Enterprise bridge.
I didn't have a specific instance in mind, just a general idea. Yeah the Stargazer has the Movie-era "Blue and green" computers, Chakotay's Val Jean has them, etc. I meant more that they never retconned that out, and there were the occasional ship we see with them in an era appropriate context.
The LCARS system is a fairly recent thing as of TNG... Stargazer still had the older style operating system, a scant decade prior to the start of TNG. Granted, Stargazer entered service in 2326, so there's a few decades there when the transition could have occurred, but still very much tracks with the 2345ish date for Mirandas still potentially rolling off the assembly line.
I don't really see them continuing production of Mirandas past the 2340's though. By the 2350's we started seeing the Galaxy class predecessors like the New Orleans class, and by the 2360's we have the larger Galaxy and Nebula classes (the latter being analogous to the Miranda class in layout.)
I think that's reasonable. I really think the "Lost Era" saw Starfleet sort of coasting on the past... they didn't seem to go hard to producing new designs. Once the mid-24th century hits, Starfleet really starts ramping up again.
The ultimate point of this being... tl;dr, all the Miranda's we see might not actually be all that old.