If you’re open to playing games on your phone, I have a couple competitive games that I can reccomend. All these games have micro transactions and battlepasses, as is tradition for monetizing mobile games these days, but they do not provide an edge over opponents, with the exception of possibly Brawl Stars. Most are cosmetic or pay to progress. None of them have any external ads you must watch:

Wild Rift - very action oriented and team based. It can be quite intense at times, so I’m not sure I would call it relaxing for most. But it’s fairly competitive.

Legends of Runeterra - From the same company, has the same characters as Wildrift, but is a card game that sits somewhere between hearthstone and Magic in its complexity.

Brawl Stars - very bright, colorful and cartoony. Team based action, with many different game modes. Similar idea and control scheme to Wildrift, but with much simpler objectives. In turn it feels much more casual. Has maybe the most aggressive minimization of the three in terms of it being in your face, but you can still play it for free.