(1) is a snapshot (ignoring color and font type) of the terminal at a given moment in time (rather than a movie, which is what script captures.)

A snapshot is a still image of a movie. The movie is typescript. The scriptreplay I posted fetaures pausing and continuing the script replay with a space bar press. There's your snapshot; there is no oher way, since terminal output has more about than color - size, movements and erasing.

You cannot get at some movie snapshot without scrolling through it. For fast scrolling, hit the + key which will increase the divisor; to slow it down, hit the - key.

(2) as if the terminal had no buffer size limitation

The buffer grows and shrinks. Is the buffer state to be considered before or after a user hit <Ctrl>L or typed "clear"? The buffer also remains static while copious typing is sent to the terminal - e.g. editing text with vi. No scrollback buffer involved, it all happens at the same buffer location.

(3) is editable and searchable with a text editor, (4) is the output of a command-line program, not the result of copy/pasting with a mouse.

Your wish (3) cannot be fullfilled, since terminal output isn't text - it's not linear. A terminal is a screen area in time. Take command line editing, going back and forth inserting and deleting chars. At which moment in time is the searched text ready to be found? Wrt (4), any command line tool which converts terminal output into streaming text will produce something between "clean text" where significant information might be lost, and the "garbage" typescript recorded.

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}