I think your Thunderbolt dock does not support DisplayLink (no DisplayLink chipset inside).
The MacBook Air M1 only supports one external display, that explains the behaviour of the dock. Your old (Intel) Mac of course supports more external displays. This is explained here:
https://www.belkin.com/de/support-ar...icleNum=317939
To get a second external monitor running, you may use DisplayLink, which is available in various docks (but only USB, no Thunderbolt) or as litte USB-adapters.
Have a look at this thread:
https://www.displaylink.org/forum/sh...ad.php?t=68010