Hi @karolis.stoncius ,
I'm glad to hear you solve the problem ,if you have any issue about SharePoint, you are welcome to raise a ticket in this forum.
By the way, since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others." and according to the scenario introduced here: Answering your own questions on Microsoft Q&A, I would make a brief summary of this thread:
[URL's search query not changing]
Issue Symptom:
Unable to update url by spfx web part in address bar
Current status:
Solved this by changing parent.location.href
directly ( parent
is the important part ), instead of using history.pushState.
You could click the "Accept Answer" button for this summary to close this thread, and this can make it easier for other community member's to see the useful information when reading this thread. Thanks for your understanding!