Scott
On the macOS desktop I use desktop client from Signal (same account as on GOS). Now I want to do the same on GOS Pixel tablet, use Signal without number (only additional client).
Unfortunately this is a no-go. Signal docs say that you can link your Android/iOS phone to Desktop or iPad, but not to another phone or Android tablet
Linked Devices
You can link Signal Desktop or Signal iPad to your phone. [...]
Multiple mobile devices and Android tablets are not currently supported.
https://support.signal.org/hc/en-us/articles/360007320551-Linked-Devices
As a workaround, you could try making a fresh Signal account on your Pixel tablet using a cheap burner number from SMSPool for SMS verification. Then forward data via messages between the two Signal accounts.
If you go this route, be sure to read through this thread for more tips:
https://discuss.grapheneos.org/d/5903-temporary-phone-numbers-for-a-multi-profile-signal-molly-molly-foss-setup