Just because you think that a matte screen is higher quality does not mean that Framework has to upgrade it. If you go back through this thread, you will see that they did consider it, but ended up deciding that a matte screen is not a priority at the time, and have not said that it has become a priority since.
For North America:
PhotoDon - Framework 13.5-inch Laptop Privacy and Screen Protectors
For EU:
ViaScreens (can ship to NA, but may take longer) - https://viascreens.com/screen-protectors/framework/
protectionfilms24 (can ship to NA, but may take longer) - https://www.protectionfilms24.com/c/ALL/framework-laptop/
BROTECT on Amazon - Amazon.de
or
Amazon.de
I’m in the US, so I can’t speak as well to the EU options, although I did order the ViaScreens back when it was the only option. Seems like others have had luck with the BROTECT screen protectors on the other sites. Photodon is the only US-based company as far as I know, and people are also happy with them.
As for cost effectiveness, that is up to you. There are many options, but depending on where you live, shipping could be more or less based on the one you choose. Many of the options also come with 2-packs, which are a great deal in case you think you might mess up the first installation, but are probably a waste of money if the first screen protector you install is perfect.
This is up to your thoughts of how much/little you want to see yourself, and how much screen sharpness you are willing to lose to achieve that. These are a bunch of posts in this thread with comparisons between different levels of matte protectors from a couple of the brands. PhotoDon will even send you a trial pack with samples of all of their protectors, along with a coupon that you can use to buy your final choice, that almost fully negates the cost of the trial pack.
Framework has not officially supported any of these brands, but Nirav posted a lot at the beginning of the thread with details on dimensions of both the full screen and the cut-out of the bezel to allow users here to buy any screen protector that fit, or to cut down a larger one to the right size.
Lucky for you, the recentish release of the Dough (previously Eve) Spectrum Gaming monitor in with a glossy finish actually caused some people to try to answer this question.
Dave2d - https://www.youtube.com/watch?v=3mTV1TOblbA
LTT - https://www.youtube.com/watch?v=MuzwlZi7FP8