Hi @karolis.stoncius ,
Per my research, We are unable to connect custom spfx web part to List web part using dynamic data. We can only connect two or more custom SPFx webpart by dynamic data. For the OOB list, we cannot write custom code with it. You could use the OOB List properties web part to connect it. We can only connect OOB webparts between each other. However there is no such function to connect a custom SPFx webpart to the OOB webparts. Here is the similar issue link
https://learn.microsoft.com/en-us/answers/questions/307847/how-can-we-connect-listwebpart-present-on-modern-p.html
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