They needed a way for him to be able to beat up the soldiers, but still have a physically obvious way of losing to the Queen, without the plot hole of why the Queen wouldn't just shoot out the holoemitters the moment he appeared.
My question would be how did Elnor's hologram end up with a mobile emitter?
VOY's Doctor acquired it in 'The Future's End' courtesy of Henry Starling who made it from the technology of the Timeship Aeon (which was from the 29th century).
In turn, the La Sirena we saw here was from the Confederation timeline (not UFP)... and given that it was mentioned in episode 2 that there is no notable mention of time travel technology for the Confederation... how did Elnor get a mobile emitter in the first place?
Unless the same timey whimey schenanigans that allowed Picard and his team to retain their memories of UFP timeline (probably by Q, or the Borgati or whatever else) retained the La Sirena from that timeline too (or at least with some internal database of it), which would only then make sense, because it is probable that SF managed to reproduce the mobile emitter and used it as the need arose.
But that's a far cry stretch of thinking if you ask me.
Plus, there's another inconsistency here. Where was Picard's brother (Robert) during all those recollection times?
The series treats him as if he never existed (not even a mention that he might be away or something).
As for the rest of what transpired... I had a thought something like this would transpire with the Queen and Jurati.
Now the only unresolved issues are Q, Soong (his daughter) and the Picard's team return to the future... which will probably be affected by Q... or Tallin will manage to provide her ship (if she has one).
In fact... on that note...given Q's loss of his powers, its possible that Tallin will provide them with a ship to get back to the future... and the team will take Q with them (who will probably be used to calculate the time vectors needed to return).
Also, some people here mentioned that Q 'must' have retained some of his powers given his insertion into FBI, VR and doing other things.
I posit that this is not necessarily accurate. With or without powers, Q still has access to all his knowledge (or most of it).
This would have been MORE than enough to allow him to manipulate technology of the early 21st century and grant him access to all kind of things.
After all, programming an interactive version of himself in VR would have likely been a piece of cake for him, and he may have put some things into motion by using his powers before he began losing them.
Similarly, he could have hacked into the FBI and given himself high level access.
Plus, when he contacted Soong, he was using technology to do everything.
So, all of the things we saw Q do in the 21st century were likely technology assisted because he has ridiculous amount of knowledge of any species in existence still in his (increasingly mortal) brain.