If you copy a reply which contains quoted text, the quoted text is removed automatically (not copied), so when you paste the copied text, it can lack important context.
Therefore it might be better to include the quoted text when you copy a reply. (I don’t think it’s important if it’s not a dynamic quote linking back to the original message or if the name of the person who wrote the original quoted message is absent.)
Do any other messengers do this?
E.g. if someone asks “what is the password?” and someone replies with a password, you want to copy just the password and including a quote in the clipboard can be annoying.
first of all: all this is about mobile, in Delta Chat Desktop you can select any text using the mouse, also in quotes
Do any other messengers do this?
i just tried WhatsApp and Signal on iOS - that has the same behaviour as Delta Chat. Same for Telegram, which, in addition to WhatsApp/Signal, allows to modify the text before coping - but i did not manage to copy the quote even there.
E.g. if someone asks “what is the password?” and someone replies with a password, you want to copy just the password and including a quote in the clipboard can be annoying.
i also think, the current behavior makes sense - i was more often happy that the copied text is “clean” than i was unhappy that the quote is missing, and this is also what i observed when watching other users. probably, this is also what WhatsApp/Signal/Telegram found out 
for the context: the text is copied to clipboard only, it is not shared or is otherwise uneditable. one can add any context needed. and if the original message still exist, one can even tap the quote and copy the text additionally from the original message
@link2xt and @r10s you make a good point that copying text without the context is sometimes prefered (maybe even most of the time). But I also find there are cases where missing context can make the copied text confusing, and manually adding context can be onerous, for example when copying a series of messages, and later reading the pasted text to see that later paragraphs suddenly change the topic or answer “yes” or “no” without providing any hint what this refers to.
I don’t know whether it is worth the effort to address this use case, but here are some suggestions that would give users some flexibility:
Have a toggle in the setting for “include quotes in copied text”, which could be set to “disabled” by default, if this is what most people prefer
Long press the “copy” icon to access a drop-down “copy with quotes” option
When a message with quoted text is copied, show a dialog box asking the user whether to include the quoted text or not. (However, I assume that Delta Chat developers prefer to avoid dialog boxes if they can, so probably this is not the best option.)