Buying a properly refurbished Logic Board will be expensive and buying a used Logic Board from an unknown source is extremely risky for multiple reasons (the board may have hardware issues, or the board may have a firmware lock, or controlled by an MDM).
Plus, like I mentioned previously, most likely other parts also contain liquid damage which may need replaced. The laptop also contains fragile easily damaged connectors so you may even accidentally damage something.
While I understand having limited resources, it seems to me that limited resources are best spent putting them toward another laptop. Putting money into this damaged laptop is extremely risky and you may lose the money by having an expensive brick (plus which part or parts do you replace?). If an Apple laptop is too expensive (they have multiple models at various prices and specs), then there are other non-Apple brands out there which may be a bit less expensive (just make sure to get a popular business class laptop as they tend to be much better built, but will cost more than the majority of the cheap junk models available...may require some research).
You can try purchasing a used MBAir 2015 model, but this is not without its own risks and may be nearly as expensive as a new model (again, money better put towards a new system which has a warranty). You would need to confirm there is no firmware lock and it is not being managed by a previous owner....the latter is harder to detect and sometimes may not show up for days or weeks. It would allow you to install your current SSD and be back up and running. Who knows whether the used Mac is working properly, or whether it may have intermittent issues which may not show up in time to return it (assuming returns are even allowed). In order to use the SSD, you would need to have the same exact model year laptop since macOS can sometimes tell an SSD was not made for a certain model Mac (I think a 2017 model would also work, but I have never tried it).
As for the files on the internal SSD, you can remove the SSD and install the SSD into an OWC Envoy Pro Enclosure (not cheap, but about the only option available...they sometimes have a used or open box one available for a bit of a discount) so you can connect the SSD to another Mac externally to access the data.
Also, you should never be worried about losing data when a computer fails. People should always have frequent and regular backups of their computer and all external media (including the cloud) which contains important & unique data. It is also best to have at least one backup which can be accessed from any computer (even a Windows system). Keep in mind that later Macs do not have removable SSDs so you will end up losing data if you don't have backups.
