How can I know which bundle provide a specific file?

With Fedora, it’s rpm -qf, which shows things like:

[root@3d1b557051c1 /]# rpm -qf /usr/bin/bash
bash-5.1.0-2.fc34.x86_64
[root@3d1b557051c1 /]#

With Archlinux, it’s pacman -Qo:

[root@79ebe49c1127 /]# pacman -Qo /usr/bin/bash
warning: database file for ‘core’ does not exist (use ‘-Sy’ to download)
warning: database file for ‘extra’ does not exist (use ‘-Sy’ to download)
warning: database file for ‘community’ does not exist (use ‘-Sy’ to download)
/usr/bin/bash is owned by bash 5.1.008-1
[root@79ebe49c1127 /]#

With Clear Linux, what command would I need to do to figure out who owns (bundle) a specific path?

I am not sure if this is what you are looking for because it may print more information than you wish for. But you may try swupd search-file. From the swupd manual:

search-file string
Search for matching paths in manifest data. The specified {string} is matched in any part of the path listed in manifests, and all matches are printed, including the name of the bundle in which the match was found.
If manifest data is not present in the state folder, it is downloaded from the content url.
Because this search consults all manifests, it normally requires to download all manifests for bundles that are not installed, and may result in the download of several mega bytes of manifest data.

I hope it helps.