OK, we'll back up a bit. It's clear you aren't aware of what Apple has done.
The drive is formatted with APFS, a new scheme (been around since 2017) for Macs. The changes are that instead of "partitions" as you might have known them, the drive is divided into Containers, and in each Container are one or more Volumes. And shortly after introducing APFS, Apple introduced the scheme I talked about earlier, where the Macintosh HD Volume holds the system files and the Macintosh HD - Data Volume holds the User data. That arrangement allows Apple to increase security on the system Volume to protect from malware that might want to hijack your system. The beauty of having multiple Volumes in one Container is that the Volumes dynamically share the free space in the Container, which is why when you look at HD and HD - Data as separate, they both seem to have the same free space. As either uses that free space, the free space remaining on BOTH will decline appropriately. In your example, for instance, if you start with 121Gb free and consume 21 GB, then both Macintosh HD and Macintosh HD - Data will now show 100Gb free.
What I am pretty sure you have now done, by specifically pointing to Macintosh HD as the install drive, is to create a third Volume, also named Macintosh DH - Data, within that Volume named Macintosh HD. So now you have, if you look at Disk Utility:
Hardware name (whatever the harware is)
Container disk# (where # is the number of the container)
Indented Macintosh HD
Indented Macintosh HD - Data
Indented twice Macintosh HD
Indented twice Macintosh HD - Data
(sorry about the "indented" stuff, but I couldn't figure out how to have the website NOT delete the tabs/spaces I tried to use to show the indentation of the various Volumes)
What you should have done, assuming you wanted to have ONE Container with just the basic two Volumes in it, was to highlight the Container name and set that as the destination for the installation. That would have then created Macintosh HD and Macintosh HD - Data at the Container level instead of creating them inside the Macintosh HD Volume that already existed.
I recomend you start over, using Recovery, and delete the Container, which should delete all of the inclusive Volumes, recreate a new Container and let it have ALL of the free space on the drive (which should be all of the drive at that point), then restart the installation, pointing to the Container. At the end you should have one Container, with one Macintosh HD and one Macintosh HD - Data Volume in that Container. That is how it should be.
Just to show, here is what my system shows:
I have an M3 MBP, as shown in my profile, runnng Sonoma, so my system has the added "snapshot" of Macintosh HD, and the Macintosh HD is greyed out. That is because on Mx Macs, with more recent versions like Sonoma, Apple has further increased security by booting from a snapshot of the Sealed Secure Volume that it constantly compares for any deviation from what Apple has determined as "Standard." That snapshot is then mounted and booted, so I get that one extra layer in Disk Utility.
I realize that this is all different from what you might have known from before, but it is what Apple has done to increase performance AND security for users.
