Progressed has slowed significantly than when I was younger in some areas. That's my viewpoint. Other places have advanced.
Yes, but we're talking about a few decades at best in real life... not multiple centuries.
Also, virtually all areas experienced radical advancements... its just that we hadn't seen updates in some of these areas in practice (but otherwise continue to advance from a scientific research point of view - and we're seeing that things that have been 'left behind' are being updated).
If i may ask (and not that I don't agree with you)... which areas do you see have slowed significantly?
Again, a lot of assumption that 810+ years=technology explosion without considering events happening that might have impacted it, i.e. Temporal Cold War, Romulan state collapsing, and whatever long term effects the Burn would have on disrupting infrastructure.
There are a lot of unknowns so that's why I am not expecting this massive technology boom. I'm willing to wait and see how it plays out.
Even if things stagnated just after the temporal cold war and the burn... most species that were part of the federation would have still had radically advanced technologies from the 30th and 31st centuries.
The Temporal Cold War also ended with the timeline repaired - ergo, any potential damage caused by Time Travel would have been undone - and technically speaking WAS undone when NX-01 put a stop to the Na'Khull.
As for infrastructure... replicators, transporters, etc. alone would decentralize things pretty heavily for every member planet... you'd have manufacturing machinery in your own home if you had a replicator (which most Federation citizens had access to in the 24th century).... and there's nothing stopping you from replicating smaller parts of a larger machine and then assembling it with even basic robotics... and the future had programmable matter to work with (which seems pretty wide-spread).
I don't think the Burn would cause much/any damage to the infrastructure on a planet because technology on a planet probably wouldn't use dilithium and M/AM reactors for safety reasons (even starbases didn't use M/AM or dilithium for power generation in the 24th century... they mainly used advanced forms of fusion in the 24th century).
Planet-side, I'm thinking it would likely be a combination of fusion, and possibly renewable sources which are extremely potent (such as Geothermal - maybe even space based Solar).
However, I will admit we have limited data on what kind of damage (if any) the Burn may have caused to planets.
We know Trill suffered a massive decline in population, but this wasn't apparently because the Burn caused massive explosions around the planet Trill... it had to do with the fact that migration patterns would have caused large groups of Trill to be off-world when it happened... leaving them mostly separated from their homeworld with no way to get back, and others would be on Starships (which exploded during the Burn)