Ok, a few days later I can say that RTL8822BE almost works.
It survied a few standby/resume cycles, but today I got the following error, again:
[48359.557206] rtw_8822be 0000:c0:00.0: Unable to change power state from D3cold to D0, device inaccessible
[48359.558578] rtw_8822be 0000:c0:00.0: mac power on failed
[48359.558583] rtw_8822be 0000:c0:00.0: failed to power on mac
[48359.558585] rtw_8822be 0000:c0:00.0: failed to setup chip efuse info
[48359.558586] rtw_8822be 0000:c0:00.0: failed to setup chip information
[48359.559154] rtw_8822be 0000:c0:00.0: Firmware version 27.2.0, H2C version 13
[48359.576812] rtw_8822be 0000:c0:00.0: probe with driver rtw_8822be failed with error -114
So this has definitely something to do with the mainboard and PCI power management.