What exactly is the relation between Bisq and Bitcoin Core?
As Bisq is not a full node wallet, it must connect to a full node in order to be able to receive transactions and learn when a transaction confirms. Without a local instance of Bitcoin Core, it will simply connect to a random node on the internet (there are some built in discovery methods for how it can find a node to connect to). If Bisq detects that you are running a node locally (i.e. you are running Bitcoin Core as well), it will instead connect to your local node and get its information from there.
Since Bisq relies on BIP 37 which Bitcoin Core has turned off by default since 0.19.0, you will need to enable this feature by adding peerbloomfilters=1 to your bitcoin.conf file. Otherwise Bisq will be unable to receive Bitcoin transactions. This is likely the syncing issues you are running into.
For some more information about local node settings in Bisq, you can read https://bisq.wiki/Connecting_to_your_own_Bitcoin_node.