Basically, no. It seems like it is difficult to find information on this because of the different versions. I couldn't find any page ever mentioning Google Sheets API v2 or v1, so I'm going to believe only v3 and v4 exist. When this question was posted, I believe it was only v3.
The top answer gives a pretty good list of your options, so here I'm just trying to find an official link for it.
Check this question out also, it's quite similar.
Currently this is the main/only documentation we've got. Within that, this is the exact page you want, but it only offers 3 query parameters. I've tried many others on my own sheets, so this definitely does not include everything. The ones here were working yesterday, but not today.
The other option seems to be the reference for Drive API (not specifically Sheets API). There is a Drive API v2 and v3. I haven't actually tried this out - some of the queries look familiar but may not actually work.
Tidbits from these links that look interesting:
webContentLink string A link for downloading the content of the file in a browser. This is only available for files with binary content in Google Drive.
webViewLink string A link for opening the file in a relevant Google editor or viewer in a browser.
This guide for migration seems to be better than the documentation itself for what you want.
Lastly, there have been some promising lists in the Docs API, but if you have to go looking in sister products it's far from a useful reference link.
Posting as a draft, not sure when/if I'll get back to this.