Starting with brass tacks, the way I'm reading the background info, your ISP was running fibre to your property, and while they were there, you asked them to run an additional, customer-owned fibre segment from your router (where the ISP's fibre has landed) to your server further inside the property. Both the ISP segment and this interior segment of fibre are identical single-mode fibres. The interior fibre segment is 30 meters.
Do I have that right? If so, my advice would be to identify the wavelength of that fibre, which can be found printed on the outer jacket. Do not rely on just the color of the jacket, and do not rely on whatever connector is terminating the fibre. The printed label is the final authority.
With the fibre's wavelength, you can then search online for transceivers (xcvrs) that match that wavelength and the connector type. Common connectors in a data center include LC duplex (very common), SC duplex (older), and MPO (newer). 1310 and 1550 nm are common single mode wavelengths, and 850 and 1300 nm are common multimode wavelengths. But other numbers are used; again, do not rely solely on jacket color. Any connector can terminate any mode of fibre, so you can't draw any conclusions there.
For the xcvr to operate reliably and within its design specs, you must match the mode, wavelength, and connector (and its polish). However, in a homelab, you can sometimes still establish link with mismatching fibres, but YMMV. And that practice would be totally unacceptable in a commercial or professional environment.
Ultimately, it boils down to link losses, which are high if there's a mismatch. But for really short distances, the xcvrs may still have enough power budget to make it work. Still, this is not using the device as intended, so you can't blame them if it one day stops working. As an aside, some xcvrs prescribe a minimum fibre distance, to prevent blowing up the receiver on the other end. But this really only shows up on extended distance, single mode xcvrs, on the order of 40 km or more.
Finally, multimode is not dead. Sure, many people believe it should be deprecated for greenfield applications. I agree. But I have also purchased multimode fibre for my homelab, precisely because I have an obscene number of SFP+ multimode, LC transceivers. The equivalent single mode xcvrs would cost more than $free so I just don't. Even better, these older xcvrs that I have are all genuine name-brand, pulled from actual service. Trying to debug fibre issues is a pain, so having a known quantity is a relief, even if it means my fibre is "outdated" but serviceable.