In short, you're usually responsible for providing your own method of scorekeeping unless in a tournament or some other competition. My scorecard is usually a memo or other text on my phone. Sometimes I write on an index card or use the DGCR app (thanks timg). The reason I don't use the app more is that I like making lots of random notes about bad or good decisions, which discs or shots I used, bad tree kicks or rolls, lucky bounces, etc.
As you alluded to, disc golf is an "on your own" sort of game, which is part of the attraction to many of us. At the same time, you can start training yourself to keep strict score and play in a disciplined manner while on your own. That way, if/when you start playing in leagues or PDGA sanctioned tournaments it won't feel abnormal.
Holding yourself accountable in some way, even in casual play, is part of what makes disc golf fun for many. The challenge of beating your previous round scores or scoring better on each hole is what keeps me coming back.
