Prob should split to it's own thread, but ...
No, even as the bark breaks down it doesn't become CO2, it's mostly just C
CxHxOx (amongst several others, but the bulk of it is that) which primarily becomes C, H, O, H2O, some HO acids and some weird CHO (fats) depending on the species.
There's no more C on the planet than there ever has been - what minor amount drops in from meteorites is counterbalanced by the trash we launch to the heavens rather than bring home to put in the bin on terra
Trees are equal parts awesome and necessary for our survival ( in a multitude of ways ) but the notion that cutting down a tree somehow increases greenhouse gases is utter bunkum.
In the same vein it's why low-carbon steel ( low in content, not low in environmental impact for making ) being forced on the construction industry is the kind of dumb that only a zealot or gov't thinktank come up with - policy devised by people who'd never pass a year4 ( junior school for us oldies) general science multi-choice, who think Chemistry is where they pickup their prescription meds.
The increasing volume of co2 that's been measured in the last 45ish years (touted as accelerating us towards the next ice-age) has a great number of factors, some uncontrollable - replenishment of ozone, volcanic activity, succesive droughts, bug-life evolution/adaption and so on - many are controllable, even reversible - to make even a minor genuine impact would require a change of ideology in Tigers and a lot of donated infrastructure to the 3rd world.
Outsideof the pure scam that is ulez (unrelated in any way to an actual problem beyond money) Airquality is a major issue - there have been technical solutions to some of this since the 50s ( that's 19xx for any GenZs on the thread !) - whilst the %age of oxygen has remained ~21, the PPM of other crud is a concern, everything living being able to continue to breathe is significantly more important IMHO.