I think I may have stumbled on something. When working in Outlook NEW and going through the process above, before I pasted the email signature block i created in Word into an Outlook message, I went to my settings and changed this.
When in your message and in outlook online, click on the Gear icon top right

in the search dialog box, type "paste" and select "Cut, copy and paste" from the selection.

In the cut, copy and paste section, make sure that "Keep source formatting" is selected for both as your default

then when you copy out of your word document where you have created an email signature (and i suggest you do this in a table as it seems to hold together better) copy by selecting and ctrl C and then paste into your email OR into the signature dialogue box with Ctrl V. It has worked for me. I did have an image in my signature, and i had to save that separately out of my word email sig setup and then insert by doing this.

Good Luck and Merry Xmas!