I'm using Safari 11 but haven't noticed that problem. Have you tried deleting cookies from those sites and clearing caches? Deleting cookies will force you to sign in again, but perhaps Safari's password memory will stick this time. Just a thought.
OS 10.15.3, iMac Retina 5K 27-inch, late 2014, 3.5 GHz Intel Core i5, 1 TB fusion drive, 16 GB RAM, Epson SureColor P600, Photoshop CC, Lightroom CC, MS Office 365