Resolved !
I finally ordered 2 of these (https://www.aliexpress.com/item/2PC-Lot-E01-ML01DP5-nRF24L01-PA-LNA-Long-Range-2-4GHz-RF-Wireless-Transceiver-Original/32797433295.html?spm=a2g0s.9042311.0.0.wuTpjZ) . Thanks @Nca78 for recommending them earlier.
I plugged them on my base modules and did my usual test.
The range is now way beyond my needs! I have 100m+ of range (I was too lazy to take the boat to cross the river at the bottom of my property..)
I'm a bit bitter to have wasted so much time but very relieved too. I have the feeling that radio will not be an issue anymore (and so I'll save hours of troubleshooting)
I've got a few conclusions:
_ It's good to ask help: thanks @Nca78 and @Yveaux !
_ As mentioned earlier in the topic with @Yveaux I think the modules recommended on the mysensors websites should be changed to these ones (or at least others that have been tested and work). Yes they are more expensive (3.4€ in my case) but it's still cheap and definitely worth the saved dozens of hours trying to figure out the radio issues. I'm also sure it would help not losing new users that get too frustrated
_ I think the whole set of tips/tricks to improve the range of some modules (solder, capacitors, clean power source, base module...) can be a bit of a trap. I don't deny that it can help marginally or drastically on some modules. But my experience has proven that even with all of these tricks applied it still would not make it with some modules. Even with modules advertised as "long range". As @Nca78 said it in is very first post, if we know that some modules just work "out of the box" we should stop recommending dodgy ones that can sometimes be fixed with tricks or not.
If I have the motivation I may even try to remove the base modules (making sure I still provide 3.3v and not 5v) and will see if they're still needed with my new radio modules.