The image is known as a cable snake:

From the author’s blog:

GNOME Shell

The GNOME shell bits to enable Thunderbolt 3 support were merged some
time ago and made it into 3.28. This means that the GNOME shell will
act as authorization agent and will automatically authorize new
thunderbolt 3 devices — if the user has administrator rights, is
currently logged in and the session is unlocked. It will also show a
little indicator (called the cable_snake by some) in the status
indicator section while devices are being authorized because the whole
authorization dance can take quite a while.

Correspondence from developer

I emailed the developer today and this is our conversation:

There are users annoyed with Cable_Snake icon making icons shift left and right in the application indicator top bar. Is there a way to disable the icon but keep boltd running?

This was introduced via a change in the kernel/udev, but a work-around
laded in bolt 0.9:
https://gitlab.freedesktop.org/bolt/bolt/-/issues/1566

There is an ubuntu bug open:
https://bugs.launchpad.net/ubuntu/+source/bolt/+bug/18926577

Is there a way to disable the icon but keep boltd running?

Currently not, GNOME Shell is hardwired to react to boltd’s probing
setting. Best way is to update bolt.

Some ideas of my own

I use the Unity interface where application indicators are right justified on the top bar so new apps opening and closing on the left are preferred and not a disadvantage.

For Gnome Users to prevent icons jumping back and forth the only band-aid I can think of is moving all icons to the right side. This can probably be achieved here:

• How can I order Gnome3 shell extensions at the top?

If this works, then when the boltctl icon appears and disappears on the left side nothing “jumps around”.