der Anstrich
coat of paint
A layer of paint applied to a surface, or the act of painting itself.
Die Fassade des Hauses benötigt einen neuen Anstrich.
The facade of the house needs a new coat of paint.

coat of paint / appearance
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coat of paint
A layer of paint applied to a surface, or the act of painting itself.
Die Fassade des Hauses benötigt einen neuen Anstrich.
The facade of the house needs a new coat of paint.

'Der Anstrich' is the noun corresponding to the verb 'anstreichen' (to paint). It describes both the act of painting and the result, meaning the layer of paint.
Wir müssen am Wochenende die Wände im Wohnzimmer anstreichen.
We have to paint the walls in the living room this weekend.
When saying what receives a coat of paint, you often use a dative construction: 'einer Sache (Dativ) einen Anstrich geben' (to give something a coat of paint).
Wir haben dem alten Gartenzaun einen frischen Anstrich gegeben.
We gave the old garden fence a fresh coat of paint.
The figurative meaning ('Schein' (appearance)) is often recognizable from the reflexive expression 'sich einen Anstrich geben' (to give oneself the appearance of something). The literal meaning refers to paint and surfaces such as walls or furniture.
Er versucht, sich einen intellektuellen Anstrich zu geben.
He is trying to give himself an intellectual appearance.
In the figurative meaning, the reflexive expression 'sich (Dativ) einen Anstrich geben' (to give oneself a certain appearance) is often used. 'Anstrich' is usually specified more precisely by an adjective or a noun in the genitive.
Die Firma gab sich einen umweltfreundlichen Anstrich, produzierte aber nicht nachhaltig.
The company gave itself an environmentally friendly veneer, but did not produce sustainably.
impression
'der Eindruck' and 'der Anstrich' can both describe how something comes across outwardly. 'Eindruck' is the feeling or image that arises in a person. In this figurative meaning, 'Anstrich' refers more to an outward, often superficial effect that makes something look a certain way. The word sounds somewhat more formal and is not used as generally as 'Eindruck'. They can be confused when something has a certain character only on the outside. For personal perception, 'Eindruck' is more natural; for an outward effect that may not go very deep, 'Anstrich' fits.

Die neuen Möbel geben dem alten Büro einen modernen Anstrich.
The new furniture gives the old office a modern appearance.
Am Telefon bekommst du schnell den Eindruck, dass der Kunde unzufrieden ist.
On the phone, you quickly get the impression that the customer is dissatisfied.