sprichwörtlich
proverbial
In a way that is so well known that it resembles a proverb; famous or typical for a certain quality.
Seine sprichwörtliche Geduld wurde auf eine harte Probe gestellt.
His proverbial patience was put to a severe test.

proverbial / literally
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proverbial
In a way that is so well known that it resembles a proverb; famous or typical for a certain quality.
Seine sprichwörtliche Geduld wurde auf eine harte Probe gestellt.
His proverbial patience was put to a severe test.

The adjective 'sprichwörtlich' (proverbial) is derived directly from 'das Sprichwort' (the proverb). It describes a quality that is so well known or typical that it seems to come from a proverb.
Sein sprichwörtlicher Geiz ist in der ganzen Stadt bekannt.
His proverbial stinginess is known throughout the whole town.
How it is used in the sentence helps distinguish the meanings. If 'sprichwörtlich' (proverbial) comes directly before a noun, it usually means a famous quality. If it appears as an adverb with the verb, it emphasizes a statement and means 'buchstäblich' (literally).
Ihre sprichwörtliche Gastfreundschaft ist unglaublich.
Her proverbial hospitality is incredible.
In its first meaning, 'sprichwörtlich' (proverbial) is often combined with well-known character traits. Typical phrases are 'sprichwörtliche Geduld' (proverbial patience), 'sprichwörtliche Ruhe' (proverbial calm), or 'sprichwörtlicher Fleiß' (proverbial diligence).
Selbst in der Hektik bewahrte er seine sprichwörtliche Ruhe.
Even in the hectic rush, he maintained his proverbial calm.
The use of 'sprichwörtlich' in the sense of 'buchstäblich' (literally) is especially common in colloquial speech. It is used to intensify a statement that is often figurative.
Nach der Party sah die Wohnung sprichwörtlich aus wie ein Schlachtfeld.
After the party, the apartment literally looked like a battlefield.
typical
'typisch' and 'sprichwörtlich' can both express that a quality is very strongly connected with someone or something. 'typisch' is more neutral and fits many everyday situations. 'sprichwörtlich' is stronger: it says that a quality is very well known, almost like a fixed image or a familiar proverb. If you only want to say that something normally fits a person or thing, use 'typisch'. If you want to emphasize an especially well-known quality, 'sprichwörtlich' fits better.

Bei der Veranstaltung zeigte sie wieder ihre sprichwörtliche Ruhe.
At the event, she once again showed her proverbial calm.
Das schnelle Aufwärmen ist typisch für Davids Training.
The quick warm-up is typical of David's training.