I concur with
@Blu€ succinct overview. Caroline really won this on her mental fortitude, as she was making more errors than usual and her serve wasn't there except for the end of both sets.
Siniakova started very strong, with excellent first serves and even second serves that Caroline could not return. In response, Caroline was holding in her service games with great difficulty. After 2-2, which Caroline was fortunate to have, Katerina's level dropped a bit and Caroline raised hers, forcing more errors from Katerina and getting the break for 3-2 on her 4th breakpoint in that game. But Katerina broke immediately back, despite Caroline making it to deuce from 0-40. Caroline broke immediately again, and briefly found her serve to get the next game at love for 5-3. Katerina held easily, and the last game of the first set was a rollercoaster, with Caroline missing first three setpoints, then saving two breakpoints, before finally closing the set.
The second set was initially an exchange of seven consecutive breaks, with Caroline serving a lot more poorly than Katerina, but also making a lot fewer errors. There were 4 breaks for Caroline, 3 breaks for Katerina, until finally Caroline found her serve, had an easy hold for 5-3, missed two matchpoints on the next game, and closed the match at love.
I think Caroline was affected by tiredness and possibly her thigh injury (still strapped). She wasn't moving as well, and although her backhand was good, she made several forehand errors of the kind she used to make when she was losing matches, and gave several short balls. She will need to address these and the consistency of her serve if she is to prevail again against Radwanska.
As for Katerina, I was really impressed with her power and quality of her shots, and her serving which was a formidable weapon when it was at its best. She seemed to make some poor choices resulting in errors that would be uncharitably called braindead in the forum, but really are most likely due to inexperience. Having watched exactly one match of hers and Osaka's (so others can correct my impressions), I find her a much more complete player than Naomi, if somewhat annoying due to her loud on court exclamations.