The 710s are owned by Rail for London, who are wholly owned by Transport Trading Limited, which is a subsidiary company of TfL. Presumably Rail for London are obliged via the contract with Bombardier / Alstom to complete payment for the units, if not already done so, and to pay for ongoing costs of ownership - eg storage, maintenance, etc.
So you'd think that Rail for London / TfL would want to see them put into service, in order to to get a return on their investment, and to minimise ongoing costs not covered by income - eg for storage - especially if they're in 'warm' storage. In extremis, I suppose they could explore selling them - though whether another TOC would want a small fleet of non-standard units is pretty questionnable. Either way though, these costs are probably a drop in the ocean within the overall scheme of TfL's funding, and there's no shareholders banging the table demanding action, which may explain the drift.
Perhaps (a bit speculative - sorry mods), London Overground are awaiting post-pandemic travelling patterns to stabilise, feeding into a recast of London Overground's timetables and a more definite understanding of the number of units required? This could also be informed by completion of any aspirational infrastructure enhancements being completed, eg to support more frequent services in certain sections.