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.". So, I would make a brief summary of this thread.
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!
[New Experience SharePoint Server only works on my Firefox, not on my Edge (works on others' Edge)]
Issue Symptom:
OP clicked the "Return to Classic SharePoint", then no longer view the new experience in the MS Edge.
However, when in the Firefox, OP has the new experience view.
Current status:
OP clears cookies and now new experience working as intended. Likely will have to manage cookies specifically to this intranet site.