GDB in a .deb package...Python?

I am part of a team creating a COBOL front end for GCC, and we've reached
the point where I am modifying GDB so that when debugging a COBOL inferior
that has a data definition

"01 hyph-var picture S99V99 value -1.23."

the GDB command "print hyph-var" properly displays "-01.23"

(Programmers familiar with COBOL won't be surprised by that.  The rest of
you will scratch your heads and say, "I sorta see what's going on there,
but..." which happens a lot with COBOL.)

I should mention that the GCC steering committee has accepted our front
end. We are currently starting to send the patches to GCC to incorporate
that front end.  And before too long I am going to be asking here about
how to go about getting my work on GDB incorporated into the source code.

But that's not important now.

What is important is that I have reached a point where I want to release
my modified gdb-cobol into the wild for alpha testing. I have created a
CI/CD process on our gitlab instance
(https://gitlab.cobolworx.com/COBOLworx/gdb-cobol) that builds a .deb
package for my gdb-cobol in a schroot environment that happens to be
running on an Ubuntu 20.04 LTS instance, and it has Python3.8 installed.

After I install that package on an Ubuntu 22.04 instance that has Python
3.10.12 installed, when I invoke the gdb-cobol executable I instantly get
the message:

"gdb-cobol: error while loading shared libraries: libpython3.8.so.1.0:
cannot open shared object file: No such file or directory"

Running ldd on the gdb-cobol executable unsurprisingly reports

"libpython3.8.so.1.0 => not found"

I am about to start exploring solutions to this problem, because I need to
be able to create a .deb package for machines that are not under my
control, and I won't know what version of Python they have installed.

But I figured I'd ask:  Can somebody let me know what I have to do to
eliminate that problem?  

(The first thing I am going to try is incorporating the relevant library
into the .deb package.  But if there's a better way, I'd like to know
about it.)

Thank you very much.