I have a Logitech Keyboard K780 and a Logitech M720 Triathlon. I connect both using Bluetooth.
Sometimes they get stuck after login or after leaving the PC unused for some minutes.
I need to go to Settings → Bluetooth so both keep working as usual, but sometimes it even doesn’t work and I’d need to manually select each device in Bluetooth config, disconnect them and connect them again.
My Bluetooth receiver: ID 8087:0025 Intel Corp. Wireless-AC 9260 Bluetooth Adapter.
For some it seems they have no problems with bluetooth devices. For others it seems bluetooth gets disabled when the system goes to sleep, or as you note may even not be properly initialized when logging in.
I personally use logitech keyboard (K350) and mouse (M570 MX Ergo trackball), but both are using the unifying receiver by USB and I have never had an issue.
Many bluetooth devices also use the wifi card for connection and wifi/bluetooth is disabled when the system sleeps/suspends. Bluetooth is a convenience for many things, but seems often to present a problem for keyboard/mouse input. Audio devices also have to reconnect to bluetooth after sleep/suspend though the user seldom notes it the same as input devices.
I’ve been experiencing a similar issue for about two weeks now. I’ve been using a Logitech K380 keyboard with Fedora for three years, and I haven’t encountered such a problem before. Every time my laptop (Lenovo ThinkPad T490) goes to sleep or restarts, I have to remove the keyboard from Bluetooth devices and reconnect it. I have a few other Bluetooth devices, but this issue doesn’t occur with them.