Macs can mount FAT if they have PC Exchange, which I believe started to be included in System 7.5. But you really, really do not want 7.5 on a black and white 9" Mac...

I would suggest asking on a vintage Mac forum because I think you're missing something existential. Generally, the classic MacOS really, really doesn't like the presence of a file system it can't recognize. e.g. if you insert a floppy it doesn't like, it will either format or eject it. Those are the only two options. So... if it seems unbothered by a Zip disk with a file system it doesn't know how to read, that suggests to me that there is a bigger issue about it recognizing the zip drive properly in the first place.

Transmac is a PC app I have used to read/write/format Mac drives and cdroms . The older versions like 7.5 will run under Win95 and the very old v3.1 16 bit will run under Win3.x and do support ZIP drives but it has a learning curve.....have used it working with Mac drives and disks before. It will work with HSF and HSF+ formats..
Yeah I still have a Power mac 7300 that was used more to work with disks for older Quadra840 and 6112CD back long ago.... working with a Classic II would be best with a mid-late 90's Mac IMHO

Transmac sounds like the answer! Shall try V4.1 from https://archive.org/details/tmac41c_zip

The Mac does read normal 720kb floppies but leaves all files in "PC" format. I can also read fine Mac floppies using FluxEngine + greazeweasle board but for some reason always fail to write 800k images.

Basilisk II with SCSI pass-through. It can talk "Directly" with the zip100 on your windows box, and can be used to create/read/write HFS on the disk in it.

Use in conjunction with "silver lining" from Mac Garden.

Make a single disk that is HFS, and use it to port over the needed utilities and disk image files from the apple support site for PC-Exchange (using Basilisk II, and it's "my Computer" mountpoint option), as others have pointed out. Then you can use FAT format for the other disks you use with it, and use windows natively with the other zip100 on the mac.

EG-- this process:

Set up a fake mac quadra or classic with Basilisk II.
Set up scsi pass-through.
Set up "My Computer" shared folder
Download silver lining
Use silver lining to set-up a disk in the zip 100.
Copy PC-Exchange and pals onto this disk.
Shut down the fake mac, and put the prepared zip100 in your real mac.
Use it to set up PC Exchange and pals. (Might as well get silver lining on your real mac at this time also!)
Use FAT format zip100s after this.

My only SCSI device is ISA card currently on 486 - with windows 3.1 / 95 I guess it is not going to work? I have a P3 with ISA and windows 2000 - would that work? Is it possible to have DB25 SCSI port on a modern pc?

The LPT flavor zip100 driver for win9x (I assume this is win9x with a zip100 on an LPT port-- if this is NT or XP, I think it still shows up as a SCSI disk) presents as a SCSI disk, as far as Basilisk II is concerned.
It will show up in the scsi disks list.

As for "DB25 scsi port on windows PC" -- YES-- A simple adapter will suffice. You can then use an external DB50 scsi cable (which is what one would normally find, IIRC, on an older SCSI card? If not, then chaining adapters for the compact scsi connectors, or finding a straight up compact scsi to DB25 scsi adapter, would do the trick.) to connect your SCSI zip100 to your PC.

I have managed to format Zip disks via scsi isa card on windows 98 machine; but it is a lot of faff to copy files this way. Basilisk route as described above is the way to go.