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Another commenter suggested Tiny Core Linux and DSL2024, which are indeed as light as it gets, but you might find yourself limited in what you can do with them, and it's not necessary for those specs.
The next step up would be Q4OS Trinity and antiX. You should be able to get the Spotify app and your preferred web server running on either of those.
This certainly isn't as lightweight as possible, but it's more usable day to day: Lubuntu.
It takes ~400MB on idle and feels super quick and responsive on my 2009 Core 2 Duo laptop. The heaviest thing in your install is gonna be Spotify.
Similarly, assuming OP is using Linux Mint Cinnamon Edition, they could try out the much lighter Xfce Edition.
Xfce is a lightweight desktop environment. It doesn’t support as many features as Cinnamon or MATE, but it’s extremely stable and very light on resource usage.
I have used Linux Lite which also uses XFCE, but I found the system to feel far less responsive than Lubuntu on my old laptop. Ymmv though.
I think i am using Cinnamon. Is there a way to switch to Xfce without a reinstall?
You should be able to simply install the 'xfce4' package via apt or software manager. It'll install the session, desktop, panel and all other widgets.
You can then log out, use a button in the top-right corner of the screen to change your session to xfce, and sign in again.
Looks like i am already running Xfce.
Try out the Linux Mint XFCE edition. The default desktop environment in Mint is Cinnamon, which is a Fork of GNOME and uses a lot of JavaScript code and thus has high resource consumption. XFCE is very fast and lightweight, I think you will have a better experience with it.
DietPi is a super lightweight distro, and they have an x86/64 version.