Usage of api_core's retry looks good to me.

Just to check (I'm not at familiar with the Spanner library), this retries the whole transaction?

https://aip.dev/194#generally-non-retryable-codes

ABORTED: This code typically means that the request failed due to a sequencer check failure or transaction abort. These should not be retried for an individual request; they should be retried at a level higher (the entire transaction, for example).

Correct. It creates a new transaction on each retry attempt.

This looks reasonable but it would be good to add a description to this PR to explain why this came about.

Done.

Also, the retry logic in run_in_transaction looks quite different. It takes the retry config into account and does exponential backoff. Will this method of retrying take this config into account?

The difference in logic is because PDML transactions cannot be committed or rolled back. This means much of the handling in run_in_transaction does not apply here.

This method currently does not take the config into account. I'll add that in shortly.