If left in the french press, the coffee will continue to interact with the grounds even when they're pressed down. This is not great in my opinion but others might not feel strongly about it. To prevent this, the coffee should be transferred to a separate server to eliminate contact with the grounds completely. A french press doubling as a thermos wouldn't work for me for this reason.

A v60/kalita style pour over is a bit more versatile (compared to say a chemex or the french press) because you can brew straight to a cup/thermos/server depending on how much coffee you need and whether you need to keep it hot for longer. It's also quick to clean if you decide you need more coffee than you originally thought.

Other things to consider:

Some people find french presses annoying to clean.

The filter mesh in a french press is usually bit finicky and will let grounds past it in some scenarios (quite often, might depend on build quality though). The edges can also start to fray over time which makes this worse.

A pour over requires your undivided attention for the whole duration of the brew which can be a plus if it, as you say, feels therapeutic but a minus whe you're in a hurry.

A pour over has a lot more paraphernalia (timer scales, gooseneck kettles) which a lot of people will recommend getting. These are not must-haves for adequate brewing but if you have a budget in mind maybe take these into account too.

Did you have links to specific products?