Use the Spotify artist ID[0] to find the Wikidata entry, and then grab the Tidal artist ID from the Wikidata entry to match the correct artist on Tidal. Even better if you use album IDs. (Brain explodes if you could use a song ID.)
Realistically, Wikidata may not have enough of this data populated, but it is nice to dream. And it seems plausible that MusicBrainz or similar might have enough data.
[0] https://www.wikidata.org/wiki/Property:P1902
[1] https://www.wikidata.org/wiki/Property:P4576
Edit: P1902 has 57000 uses and P4576 has 7000. So YMMV big time.