gosh, and here's me hoping you'd gone on holiday for a month

only joking - it's good to chat - a shame that no one will join in with us.

Regret I know zero about glass from the C12 - but glad to hear it's a period of special interest to you - what might be described as the middle ages of the medieval epoch do you think, or should that be the Dark Ages? Knights and damsels in distress, possibly.
In the U.K., glass making was non existent around that time, and it looks to have only got going with the Venetians c. middle of the C15. The Muranese glass workers were forbidden to travel outside of their country, on pain of much discomfort, so the spread of knowledge of glass making was very slow, but toward the end of the C16 we Brits. did give the world lead glass, courtesy of Mr. Ravenscroft.
"Getting your threads resolved" is a bit too much of an unrefined expression - members here do their best, but we are virtually all amateurs like yourself and whatever knowledge we have is limited, but we do our best by means of experience and our books. Regret I know nothing of limitations of posts for new members - I'd just keep banging away if I were you - they'll soon moan if you get it wrong.
As for buying glass and what you spend - I agree that you should buy what really turns you on - don't remotely think of glass as an investment - that is the surest way to go wrong. The main Egermann colours were red and amber, and I expect that somewhere in the east of the Continent they are still churning it out just as they did in 1840 - 50. But, age carries a massive money premium - people will pay fortunes for something that is genuinely old - and just think that if you do learn about glass you will eventually reach that day, in the market, when the light bulb goes on and you realize that you're looking at something that's early C19 perhaps and all they want for it is ten euros. It really does happen, but you must read the books, go to antiques fairs/markets and handle the glass - it's a useful and inexpensive way to learn.
The annealing process wouldn't, IMHO, cause the surface to become matte - more likely the blue was dull to start with, or some other agent has deteriorated the original lustre, assuming it had one. Glass is notoriously difficult to re-shine - it can be done but needs prodigious amounts of patience, or alternatively you need professional acid treatment .......... but then again if acid was used in the proximity of stained glass more harm might happen than good. Live with the dullness, it's part of the life of your piece of glass, which if it could speak would have such tales to tell, and no it isn't a reject - just something that has seen life and lived - do you shine all over?

Don't under any circumstances go anywhere near acid - simply isn't worth it.
Problems with annealing are possibly ......... cracks, shrinkage, distortion, but not usually a lack of shine.
The next step up in terms of quality - re coloured glass that is cut-to-clear, is the proper overlay process - have a look at some of the Val Saint-Lambert from the early to mid C20 - breathtaking beauty and skill - especially the art deco shaped/designed pieces. And then view some of the art nouveau Daum, Galle, Goupy, Baccarat deco shapes, Argy-Rousseau and States Tiffany style glass - it does tick on a bit.
If I have a favourite it's probably deco.
Know what you mean about wanting to know about your pieces - unfortunately in the glass business we have to learn to live often with anonymity and lack of attribution - this is what drives some people to collect only those pieces that come with provenance of some kind, but that's to overlook the fact that beauty remains beauty whether there's a label or not.
As for the Biedermeier style, it seems to have a smaller following here than the Continent, perhaps. I'm never quite sure how to describe the style - is it a sort of middle European arts and crafts, late French Empire fashion which came from Germany - is this your architects coat now speaking.

Something to do with the Romantic movement? or is that wrong.
Finally, as for dating your blue piece - my honest uneducated opinion is that it's more likely to be from the first half of the C20 than the second half of the C19 - but that is my humble opinion only - and just think, once you've read your books you may be able to tell us when it was made.