Admittedly, this is a real head-scratcher as to why this is happening.
I’ll start by noting that log spam is a known quirk that was a workaround for a bug in ESPHome.
This has been fixed (expecting it to hit in 2024.8).
That said, the log-spam should have no impact on functionality.
If you’re experiencing disconnects, it would suggest you’re in an RF-unkind environment.
As such, you can find the instructions to disable the WiFi power-save which should result in a more stable connection here LocalDeck Disconnects - Sending keepalive failed!