A dedicated global compose key solves this problem very elegantly. Hitting the ◆ compose key (right alt for me) followed by a series of intuitive characters inserts the corresponding character.
For example:
◆ - - - produces an em dash (—)
◆ - - . produces an en dash (–)
◆ ' e produces é
◆ | c produces the cent symbol (¢)
Usually, you can just guess the combination and be right 3/4 times. Otherwise, it's fairly easy to look it up, or create it if it doesn't exist yet.
Some distros of Linux have this built-in, but I use WinCompose[1] on Windows.
macOS has something very similar with the option key, but the set of characters doesn’t include all Greek letters which is incredibly annoying: https://sites.psu.edu/symbolcodes/mac/codemac/
Also works in the Julia REPL, and jupyter notebooks. I'd hope that the tooling for any language which allows unicode variable names would support this.
Emacs has this plugin (well not a plugin because it’s built in). One can select an input mode. Some translate directly (e.g. a Greek input mode where typing a gives an alpha). There is also a TeX mode like what you describe and another mode which is more concise (e.g. &a for alpha, where the means Greek). The difference from what you described is that instead of some escape sequence for these special prefixes, they are just never converted if they don’t match and you move the point away.
You press the backslash key, enter the name of the symbol, then press enter, and the symbol will show up in your buffer.
Something like:
\lambda -> λ
\Lambda -> Λ
\\ -> \
et cetra.