freeze in 30-60 seconds on a macOS Catalina when connecting bluetooth headphones

Hello everybody, I use a MacBook Pro 2018 (Catalina 10.15.7), the lags started a month ago and to this day they enrage me.

The problem itself is that when you connect any bluetooth headphones (JBL Live650BTNC or AirPods with wireless charging case), a freeze occurs (not every time, but very often),I can not play any audio, video or reload a web page, the whole browser freezes, and the system starts to strain, after 30-60 seconds Safari starts working and everything goes back to normal. ALSO, there were some random headphone disconnections in the middle of work.

I tried all the methods: I completely rebooted the bluetooth, deleted the .plist, rebooted NVRAM or PRAM and SMC, downloaded Hardware_IO_Tools_for_Xcode and, using the Bluetooth Explorer utility, made a force restore, switched to another profile, it had the same situation. I noticed that this problem manifests itself in the second half of the working day, when the Mac is more loaded, perhaps this affects.

Sometimes when cleaning junk with Clean My Mac, everything returns to normal.

Here are some logs from the console at the moment of unsuccessful connection of headphones:

• error 18:00:02.662935+0200 com.apple.WebKit.WebContent 0 is not a valid connection ID.
• CoreBluetooth isn't advertising for client type 9
•  AudioObjectAddPropertyListener: no object with given ID 0
•  AudioObjectHasProperty: no object with given ID 0
• fault 17:33:46.413083+0200 Google Chrome Helper (GPU) Couldn't read values in CFPrefsPlistSource<0x7fab1ee07570> (Domain: kCFPreferencesAnyApplication, User: kCFPreferencesCurrentUser, ByHost: No, Container: (null), Contents Need Refresh: Yes): accessing preferences outside an application's container requires user-preference-read or file-read-data sandbox access
• error 17:34:18.737067+0200 kernel Sandbox: bluetoothd(170) deny(1) mach-lookup com.apple.server.bluetooth

Software installed on my laptop(maybe this will help): VS code, Skype, Telegram, ZXP Installer, AppCleaner, Backup and sync from Google, CleanMyMac X, Figma, Macs Fan Control, coconutbattery, Nicepage, Discord, MongoDB Compass, uTorrent Web, VLC, Postman, Spotify, Keka, Trello, zoom.us, Adobe Package, steam, Upwork, NTFS for Mac, Bluestacks, Chrome, Opera, MAMP, Viber, Turbo boost switcher, Final Cut Pro, Disk Inventory X, Cinebench, Flume, Color Note, and the rest of standard programs...

Maybe someone has encountered this problem? The only way out that I see is reinstalling macOS, but maybe there is another solution?