I actually admire you for being able to tell a difference, and trying to confirm it. Most people these days seem to drop $300 or whatever on wireless ANC headphones and insist that they are incredible because they are 'expensive'.
If you don't like the sound, there's nothing that can really be improved from a hardware perspective. The headphones themselves have some pretty hard physical limits imposed by being closed back, and (probably) having some pretty small drivers, and prioritising space and BoM for BT and ANC electronics + batteries. Fundamentally, these were
not a product built for high sound quality, they were built for
acceptable sound quality and ANC. These are all about the ANC, there is no other reason to buy this kind of product.
The one thing you might try is software EQ. This is... unlikely to help if you find the sound muffled, but you should be able to try EQ without cost or hassle.
So, now when we touched the subject of wired headphones, DAC amps etc would you say that if I would get some external DAC for my phones it would produce better sound? Would I plug it to my pc's soundcard or would I need to buy some better external sound card?
Why people have those DACs anyway? Sorry, don't know anything about those, but I'm intrigued
There are loads on sale for example on Drop.
Would one of these make my wired headphones sound a lot better?
Yeah, external and discrete gear can make headphones sound better. But it depends on the source material, the gear, whether the gear complements other components, and how much effort you put into listening. People talk about keyboards being a 'rabbit hole', a term which I really dislike, but keyboards are
nothing compared to higher end personal audio. I have a single pair of headphones that cost more than all my keyboards combined.
The headphone world is full of magical thinking, snake oil, and slavish trends. It's surprisingly easy to get 'good enough' but it's also easy to get trapped in a recurring cycle of meaningless, money-wasting, side grades chasing the lastest FOTM.