Install chimney as a precaution

Well, the tree dies even if we don’t cut it down and then releases the same amount of CO2 when it decomposes

1. No, not at all. After its natural death, a tree usually stands around as a skeleton for about 10 years until a storm knocks it down. Then it provides habitat for all kinds of animals and fungi and eventually gets decomposed into "topsoil" or, in a few million years, something like coal. It’s not like a tree just disappears into thin air after dying. About 20 years ago at my parents’ place, we cut down a tree and were too lazy to remove the roots. Until they sold their house, the roots bothered us every summer, until it eventually became the new owners’ problem. 2. The time horizon has to be considered. You didn’t address that. There is a nice open letter with further links under the search term "Scientists response to US advocacy for burning forest biomass," which discusses the short-term to long-term 100-year regrowth period. With those links, one can dig as deep as they want. 3. Is anyone here aware of both ecology and pollution issues? Then it’s possible to discuss burning wood purely for a cozy feeling as pure consumption. To me, that holds the same significance as cruising through downtown in the evening with a V8 and flap exhaust. It stinks, is carcinogenic, and causes lung problems or asthma. I like fire, and when the heating season starts, I still enjoy the faint smell of smoke while walking. But the further the winter goes on, the more annoying it becomes. As humanity, we’ve achieved a lot to no longer depend on burning coal and wood and have clean air. Now we’re destroying that civilizational progress as a pure luxury for individuals and allowing pollutant levels in our residential areas to rise significantly. But also here, as with everything: the dose makes the poison. With a gas fireplace, you have fire, flame, and warmth but relatively environmentally and health-friendly in direct comparison. I don’t want to take anyone’s fireplace away. Occasionally with a glass of red wine? Cool. But every evening? No. I haven’t noticed how much fire is being made in my downtown apartment so far. In the city, never. In the older, more established residential area a few meters away, many stainless steel chimneys have been installed, and it’s really annoying to walk through there. Fortunately, no one here yet has money for that fun, so we get fresh air when airing out.

Of course, one can gladly discuss that.
On point 1, you are on the wrong track. You are right that the tree still provides habitat for many animals after its death. But eventually, it does actually decompose. And during this process, it releases the CO2 that it once absorbed. Walk through a forest and look at trees that have been dead for a long time. It has to be that way, otherwise the Earth would keep getting bigger due to the plants dying every day.
Otherwise, one can of course consider whether you have to do that for coziness. But coziness is quality of life,
and then you have to question everything that brings quality of life and is not absolutely necessary. Then please also don’t fly on vacation anymore, but rather look at pictures of foreign countries on YT.
We also have a fireplace, but we actually use it to generate heat. It runs daily for us, and for that, the heating only runs at 20 to 21 degrees, which is too cold for us to sit in the evening.

And this process releases the CO2 that it once absorbed.

That's correct, but as has already been written here, the same applies to oil, coal, etc.
All of this is stored CO2 or stored carbon that is therefore not in the atmosphere as CO2.
Of course, we could revert the Earth to its original state, but that is simply inhospitable to humans.

Trees can be wonderfully processed into furniture, roof trusses, or entire houses to store the carbon there for the long term.
Here, the lifespan of the items matches quite well with the duration of regrowth.
This is not the case with burning.

Back to the topic. If money doesn't matter, spend about 10 k€ and enjoy the fire 5-10 times a year. Done. ;) "We don't have a fireplace because it didn't fit into the floor plan," is also wonderful. :D

to the original question:

we no longer need the existing chimneys for flue gas exhaust.

But in subsequent use, it has become part of the central ventilation system with heat recovery
and additionally serves as a riser shaft for various newer wiring.
It's quite practical, even though this was never originally intended.

That means I would provision the chimney, whatever is to happen with it in 15 years.

Thank you very much for your answers!

We will probably install a chimney to then connect a pellet stove. We think that a pellet stove operates somewhat more efficiently and thus reduces fine dust emissions.

Have a good start into the new year! ;)