With some debugging I've found out that tramp has the correct path if
you:
- have tramp-own-remote-path in tramp-remote-path
- don't pass the `-l` tramp-login-argument up until line 5538 of
tramp-sh.el of tramp 2.7.0-pre
Here's a snippet for context of that part of `tramp-get-remote-path`:
```
;; Remove double entries.
(setq elt1 remote-path)
(while (consp elt1)
(while (and (car elt1) (setq elt2 (member (car elt1) (cdr elt1))))
(setcar elt2 nil))
(setq elt1 (cdr elt1)))
```
It looks like this when tracing `tramp-send-command-and-read` and
`tramp-get-remote-path`:
```
1 -> (tramp-send-command-and-read (tramp-file-name "docker" nil nil
"nifty_davinci" nil "" nil) "echo \\\"`uname -sr`\\\"")
1 <- tramp-send-command-and-read: "Linux 6.1.18"
======================================================================
1 -> (tramp-get-remote-path (tramp-file-name "docker" nil nil "nifty_davinci"
nil "" nil))
| 2 -> (tramp-send-command-and-read (tramp-file-name "docker" nil nil
"nifty_davinci" nil "" nil) "/bin/sh -i -c 'echo
3530864d92d71ab02b08b4a1f9168a38 \\\"$PATH\\\"'" noerror
"3530864d92d71ab02b08b4a1f9168a38")
| 2 <- tramp-send-command-and-read:
"/root/.cabal/bin:/root/.local/bin:/opt/ghc/9.4.2/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin"
1 <- tramp-get-remote-path: ("/opt/ghc/9.4.2/bin" "/usr/local/sbin"
"/usr/local/bin" "/usr/sbin" "/usr/bin" "/sbin" "/bin")
======================================================================
```
