Kind of, the way discord webhooks is that you’d have to send a POST request to the discord’s webhook URL.
That’s the same case for your own personal database, make a POST request to your database URL and the rest will be handled with your external server/script.
If you’re planning to use services such as Google Sheets, you’d have to keep in mind of their rate limits. For example, google sheets has a rate limit of 500 requests per 100 seconds per project. However; if you were to host your own MySQL database via (eg; glitch) and you’re a premium glitch user, you’d get unlimited requests so you won’t ever be rate limited.
Try taking a look at this if you’re planning to use Google Sheets. Ofcourse; the resource provided is not a 100% straight on guide on how to literally make a “logs” database, so you’d have to tweak some of it and make it so it fits with your use case; hence why it’s an open resource.