It can matter from a trust and safety perspective. If I do my online grocery shopping at tesco.com, I build up trust that it's reliably owned and operated by Tesco plc.
When I then hear that I could get my phone from Tesco Mobile and do a
search, I land on tesco.com/phones —
I'm clearly on the same website, so I can shop with confidence.
If I'm thinking of ...
If you want users to notice the domain switch, then switch the domain.
If you don't want them to notice they are on a different domain, then don't.
Users most likely WILL notice. (At least in Europe you will be asked for cookie consent on probably each new domain you visit.)
Does the design change significantly? Is there a completely different navigation ...
It's really a matter of how you want to market and image the parent and the brands to consumers.
Are you trying to make the brands be their own very standalone product? Then have brand.com as the website. Gatorade is an example of this. It's owned by Pepsi, but you don't see "Pepsi" on the Gatorade website.
Do you want them standalone, but still ...