Many years ago, a 2-line stand alone AT&T branded answering machine (model 1772) was available
Each line was independent of the other so 1 line could get the full treatment (answer calls and record messages), while the other side could be set up as announce only.
Here is the manual.
At one time, there were multiple answering machines available to choose from. But....with the contraction of POTS lines, the proliferation of cordless telephones and bundling of voicemail service.....stand alone answering machines have just about vanished from the market.
at&t/VTech offers 1 model (the 1739), but I don't think it has an "answer only" mode. My favorite single line models are the AT&T/Lucent 1715 (1 line/1 mailbox) & the 1725 (1 line/4 mailboxes).