If the TV has a sufficiently good web browser, you could try to download something from your NAS and measure the time taken. Your bandwidth is Data / Time. Synology should have a basic web server, I think it's name is "Web Station", to install from their "App Store". Over this, you could export a big file, such as a movie and download it from the TV.
I think, your issue is, the TV can't handle the codecs too well. Maybe you have higher bandwidth movies, than the internal decoder on the TV supports without issue. Also it could be, the Synology NAS transcodes the movie as you stream it. This can be adjusted in the settings. Most Synology NAS offerings for the home are not very powerful when it comes to video real-time conversion, depends on your model.
Mostly, very high quality videos will by far not saturate even a 100 Mbps link, which would be 10x slower than what your NAS offers and can realistically saturate (since hard drives are quite fast when transferring large data sequentially).
I would check, what the TV can handle in the specifications for it. Maybe, the TV firmware can be updated as well. For the Synology, I would check, if it transcodes anything. If yes, try turning it off. If not, try to turn it on and play with the settings a bit.