Is there an external Blu-ray player compatible with iOS13?

Perhaps you mean macOS 13? Apple likes to use the system software name “iOS” for iPhones specifically.

Many third party USB-connectable BD drives are compatible with Macs.

➔ Google search “mac external blu-ray drive”

Any BD-compatible optical drive from OWC should work fine with Mac. Mac accessories and upgrades is their specialty. Internal and external Blu-ray optical drives - OWC. Slimline or 5.25" 1U height. Note that there are read/write speed differences, USB-2 vs. USB-3 differences, compatibility with various disc capacity sizes and types, and sturdiness differences (slimline may not be the best choice for heavy duty).

Writing to disk may need its own authoring (and burning) software, when creating video discs for compliancy with the standards (so that your home video can play at a friend’s house).

➔ Google search “mac blu-ray authoring software”

While you can read from and write to various capacities and various disc type Blu-ray discs through Mac, in any format and structure that you have prepared, there isn’t much Blu-ray video playback software for computers with a user experience on par with set-top Blu-ray players, for watching commercial BD titles. E.g. disc menu navigation seems to be a weak point, and thereby access to some features.

➔ Google search “mac blu-ray player software”

For watching commercial BD titles, I would advise a TV-connecting set-top box instead.