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Sage caches the GAP workspace on first startup to improve its startup speed. There's a command gap_reset_workspace (docs), after which gap() will recognize the transitive groups of order 32:

sage: G = libgap.eval(f"Group((1,2), ({','.join(map(str, range(1, 33)))}))")
sage: gap(G).TransitiveIdentification
2801324

However, libgap still didn't seem to recognize the groups, possibly due to needing to be recompiled. Because I had installed Sage with mamba, I didn't have an option to rebuild, so I:

1. upgraded mamba past version 2
2. git cloned Sage and changed to that directory
3. created a new mamba environment with Sage dependencies installed
4. placed the data for transitive groups of order 32 in the transgrp directory
5. built Sage following the above instructions

Afterwards, libgap recognized the transitive groups of order 32. Hopefully, if I had built from source originally, calling make build or pip install --force-reinstall after placing data in the transgrp directory would result in libgap recognizing the groups, but I decided to place the groups there ahead of time, just in case that didn't work.