I mean, I like the Lara Croft thigh holster route, but that might chafe.

And if you're wearing it the way the male model is, you can probably add an outer shirt or jacket and wear it like an underarm money belt in less-secure environments. I have one of those that I repurposed for carrying a tablet. Looks very similar to this, though not the same brand or type of fabric:

https://www.amazon.com/Multi-Purpose-Anti-Thief-Security-Underarm-Messenger/dp/B077GD5C27

Kind of like a very thin purse with a padded, short strap that's intended to optionally hide under one's clothes.

You don't need something that large to carry a phone, though. The sort of smaller thing that they're doing here is big enough for that.