I'm back in Ubuntu! The issue was that the path to grub set in the BIOS after the firmware upgrade was wrong. Fixing the path fixed the issue.
To do this, press the F2 key while rebooting the Dell laptop, to bring up the BIOS interface.
Optional: In the menu on the left, first select System Configuration > SATA Operation, and select the AHCI radio button. (This step is required on my machine, because there are no RAID drivers installed for Ubuntu yet. If you have RAID drivers for Ubuntu, then you can choose RAID On instead.) Confirm the change of SATA Operation.
With the correct SATA setting already chosen, select Boot Sequence, and then click on the Add Boot Option button in the middle of the right pane. Name the new record (in my case — Ubuntu AHCI) and click on the [...] button to the right of the File Name field, choose a grub file for start-up. Select EFI > ubuntu > grub64.efi. Click OK.
Using the arrows by the list at the top right of the Boot Sequence pane, place your new Ubuntu Boot Option at the top of the list.
I had a new Boot Option with an unhelpful name (UEFI: THNSN5256GPU7 NVMe TOSHIBA 256 GB, Par) which had the same choice of file as Windows Boot Manager. I deleted this, and checked afterwards that I could still boot into Windows. Here is what my Boot Options look like now:
[✓] Ubuntu AHCI
[✓] Windows Boot Manager
Click Apply, confirm your changes, and then click Exit.
The machine should now boot into Ubuntu, just as it did before the firmware upgrade.
Best Answer
Actually if it came from the Ubuntu Software Center it usually had passed some minimal security tests before it was included. So I would not be too worried on the safety. But these tests may be incomplete or somebody had overlooked something. Nobody is without fail, so cautiousness always pays off in the end.
It is perfectly fine to hesitate and to be careful in what you install, or not install. A firmware update in the best case solves issues you have, in the worst case introduces issues you didn't have before. So in case you are happy with you system there is little need to risk anything.
General sources of concerns are not so much version numbers (many long established applications still are version 0.x) but
If you are faced with such an update it is good advice to perform an internet search for issues other people may have had. Even if nothing turns up then nothing would be lost if you waited a bit with the update. Sometimes bugs need their time to be published, and even longer to be fixed.
So my general advice is: if you are worried: wait !