Btw, why is the target folder 16GB after compiling? And even if I change a line in pane.rs, upon running again using cargo run, why it again compiles some of the crates which I haven't touched? (It always starts compiling from workspace crate, 1145/1193, and then takes a lot of time and CPU, and heats up my laptop).
Any way to change this behaviour?

I know rust projects are heavy, but this is too much for my laptop. I only started learning rust a few months ago and didn't expect this much from big projects 😂. Likewise, I plan to move zed repo to my external ssd to save space.

Another thing, I am using stable zed to edit the files, which is a little unusable since cargo checks every crate upon a single edit, which slows down the zed, and my laptop. I need to disable checking while writing code. Thank god I didn't open it up in VSC

Btw, why is the target folder 16GB after compiling?

This means you've compiled it too few times, you need to try a few more times, with different toolchain versions preferrably

du -h target/
...snip
189G	target

cargo and rustc need various intermediate data for incremental compilation and build creation.
In addition to that, default debug builds contain a lot of "extra" things like debug information, not-fully-optimized-and-reduced code (that could cargo --release or a differently configured linker do at cost of much more CPU usage), and Zed uses a lot of dependencies, exposing such issues more than inside an average rust project.

Whenever something in the build chain diverges (a crate version, a rustc version, etc.) — whatever's affected by that change has to be recompiled, bringing in more artefacts, debug info, incremental info, etc.
As cargo does not know the semantics of such changes, it preserves old versions (what if you just switch a branch and now switching back, wanting faster recompilation?) of old files, sometimes too aggressively by my taste.

cargo clean or, better, https://github.com/holmgr/cargo-sweep might help here

And even if I change a line in pane.rs, upon running again using cargo run, why it again compiles some of the crates which I haven't touched?

pane.rs is a part of a quite foundational crate, workspace, and now every crate that depends on workspace, transitively or not, has to recheck whether it used (transitively or not) certain modules that you've changed or not — and if you did, it has to recompile.
And, of course, the final binary has to be relinked nonetheless.

and then takes a lot of time and CPU, and heats up my laptop).
Any way to change this behaviour?

Realistically — using a different machine, either a remote one (Zed has some remote capabilities enough to work and it improves every month).

Apart from that, you could install a different linker if you're on Linux (Zed CI uses mold) and tinker with cargo profiles more, adding another near

After that — only some work on Zed's dependencies to reduce them, but not sure what are bottlenecks on your machine.

which is a little unusable since cargo checks every crate upon a single edit

There are two things: your default settings save files very often, presumably after editor's focus is lost (which might be good by itself) — that triggers the default feature of rust-analyzer, "cargo check on save", which produces most of its diagnostics currently.

So, either you could move into state of manual saves only, or tweak check on save (up to disabling it fully): https://zed.dev/docs/languages/rust#large-projects-and-performance