While it depends on how old the older computer, I recently installed LMDE 7 on a PC from 2011 and it runs fine. If that PC has an SSD, it should be fine for your needs.
LMDE is Linux Mint Debian Edition, it's basically Debian with Mint coat of paint. Also, Bookworm is old now, you should install Trixie if you want Debian, which is the latest stable version.
It actually has a graphical installation now, so you can install Debian and choose a lightweight DE inside installation. For example LXQT is quite lightweight. XFCE is also fine, though is heavier than this. By the way, I use KDE on a laptop from 2011 and it runs great. You just need an SSD.
If the PC is too old, there is a distro called antiX Linux. I don't know how it is nowadays but it's one of the fastest and easiest distros you can find IMO.