It seems that switching back to 8.12.5 helps:
$ flatpak install com.getpostman.Postman
$ flatpak remote-info --log flathub com.getpostman.Postman
Commit: 2e682ac240bf789834f69a511a7adab7412f1ca59ca4eced5778f4cafc3232a2
Subject: Update Postman.tar.gz to 8.12.5 (6b8cfd07)
Date: 2021-11-17 16:47:32 +0000
$ flatpak update --commit=2e682ac240bf789834f69a511a7adab7412f1ca59ca4eced5778f4cafc3232a2 com.getpostman.Postman