
die Brühe
broth
A clear, savory liquid made by cooking meat, bones, fish, or vegetables in water, used as a base for soups or sauces.
Eine kräftige Hühnerbrühe hilft bei Erkältungen.
A strong chicken broth helps with colds.
broth / sludge
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broth
A clear, savory liquid made by cooking meat, bones, fish, or vegetables in water, used as a base for soups or sauces.
Eine kräftige Hühnerbrühe hilft bei Erkältungen.
A strong chicken broth helps with colds.

weak brew
Colloquial and derogatory for a thin, watery, or tasteless liquid, especially bad coffee or tea.
Der Kaffee in der Kantine ist eine ungenießbare, braune Brühe.
The coffee in the cafeteria is an undrinkable brown brew.

sludge
Colloquial for a dirty, murky liquid or mud.
Nach dem starken Regen stand eine übelriechende Brühe im Keller.
After the heavy rain, a foul-smelling sludge was standing in the basement.

to stew in one's own juice
An idiom meaning to leave someone alone with the negative consequences of their own actions.
Nachdem er alle betrogen hatte, ließen ihn seine Geschäftspartner in der eigenen Brühe schmoren.
After he had cheated everyone, his business partners left him to stew in his own juice.
The meaning of 'Brühe' (broth/sludge) depends heavily on the context. In a cooking context, it is a soup base. In other contexts, the word is usually negative and describes a bad or dirty liquid.
Für die Soße brauchen wir eine gute Gemüsebrühe.
For the sauce, we need a good vegetable broth.
In the culinary sense, 'Brühe' (broth) is often used with verbs like 'kochen' (to cook), 'zubereiten' (to prepare), or 'ansetzen' (to start/prepare). Typical types are 'Hühnerbrühe' (chicken broth), 'Rinderbrühe' (beef broth), and 'Gemüsebrühe' (vegetable broth).
Ich koche die Nudeln direkt in der Gemüsebrühe, dann werden sie würziger.
I cook the noodles directly in the vegetable broth; that makes them more flavorful.
When 'Brühe' (brew/sludge) describes a bad or dirty liquid, the word is colloquial and derogatory. Adjectives like 'dünn' (thin), 'wässrig' (watery), or 'dreckig' (dirty) reinforce this negative meaning.
Nach dem Rohrbruch stand eine braune Brühe im ganzen Bad.
After the pipe burst, a brown sludge covered the whole bathroom.
The idiom is 'jemanden im eigenen Saft/in der eigenen Brühe schmoren lassen' (to let someone stew in their own juice/broth). It means leaving someone alone with the negative consequences of their actions and not helping them.
Er hat uns alle angelogen, jetzt lassen wir ihn in seiner eigenen Brühe schmoren.
He lied to all of us; now we're leaving him to stew in his own juice.
great
According to the meanings given here, Suppe and Brühe cannot be used interchangeably in this context. Suppe is used only very rarely and informally as an evaluation meaning „super“ or „toll“ (great), whereas Brühe refers to a clear, savory liquid. Suppe fits for an evaluation; Brühe for the liquid.

Für die Soße kochte sie eine klare Brühe.
She made a clear broth for the sauce.
Er fand das Konzert in diesem sehr informellen Kommentar suppe.
In this very informal comment, he said the concert was great.