I would look for coordinating beige and/or teal tile. I had posted a response when looking at my phone not realizing the black is glass block.

I would look at Daltile Keystones in Spa or Aegean for the teal, and Elemental Tan for a darker beige. You can order a mix of colors in their mosaics as well. These are replacements with porcelain.

Vinyl will be tough because most vinyl available in America is something that looks like wood or stone and it's not really right for this bathroom.

Linoleum could be an option:

These two are tile:

Forbo Marmoleum Barley

Forbo Marmoleum Shitake

Sheet will give you more options. The above plus some other neutrals like Marmoleum Fresco Camel

But they don't offer a good Teal

The big problem with trying to do vinyl these days is that all anyone is selling in the US is fake stone. You won't be able to find anything that harmonizes well with your other tile. I agree that tile is the best option.

If you feel a little splurgy and you happen to find old linoleum that you actually like under the tile when you excavate, this company will make a vinyl floor from an image, of anything you want:

https://www.atrafloor.com

I realize it's highly unlikely that you'd like the lino, even if it's there, but I thought I'd put it out there, just for fun. You could theoretically have your old lino back, but in vinyl. I have no idea of their prices for custom, but their regular work is all to-order, and the prices aren't outrageous for a bathroom-sized floor.

ETA If you like the idea of marmoleum, forbo offers some other interesting colors:

https://www.greenhomefloors.com/Forbo-MDS-Marmoleum-Linoleum-Roll-Sheet-Flooring-79-Wide-25mm_c42.htm

but they are mostly in the sheet marmoleum and I believe that installation can be expensive for that.

Mannington's Revive Collection offers some fun vintage and retro looks if you are set on doing a sheet vinyl floor.

https://www.mannington.com/Residential/LuxuryVinylSheet/Search?FilterCollections=0

Looking at replacing white tile with sheet vinyl.

Do I understand you're keeping the wall tile? If so, I'd say go with tile on the floor too. You can go the other way around -- tile on the floor and something "lesser" on the walls, but I don't think it will work as you're proposing.

If you go with tile, I'd say replace with what you already have: A simple white square.

Tile is always better than vinyl.

Eh, maybe. It is a more durable product, and it will add more value to the house ... but I like the vinyl in my kitchen (which is softer underfoot, easier on the feet and knees, and doesn't break things I drop) better than the tile in my bathrooms (cold to the touch).

@ Mrs Pete, I always wear slippers in my house. Plus my floors are heated so tile is even better to retain heat.