Should you answer 'are you interviewing elsewhere' honestly when you don't have other interviews yet? A bit of context. I am about to get my PhD soon and a few months ago I started applying for R&amp;D positions1  , both in academia and in the industry. A few things to note here:

I am interested in applying to positions in a limited number of countries (in Europe)
The positions I applied to may be very competitive (especially the ones in industry)
The COVID situation may be impacting the job market

So the result is that I ended up with a very limited number of applications (~15) and absolutely no feedback from them, except one rejection and one invitation for an interview. The latter is in an academic research lab.
Now I have been thinking, if in this upcoming interview I'm asked: “Are you currently interviewing elsewhere?”, should I be honest and say that I’m not?
My concern is that I don’t know how this could be seen. I thought of 2 options:

they will think that I’m not “in-demand” and that I don’t have successful applications so perhaps that may discourage them from hiring me.
they instead would be understanding of the fact that I don't have other options, given the global context and my personal preferences. Then, if the interview goes well and they do make an offer, I'd have to provide them with a response fast since they know that I don’t have other options. My concern here is: what if (miraculously) another/better option opens up for me in the meantime such that it would be better for me not to respond to the first offer right away.

Note that my question is not very related to: Should I tell other interviewers where else I've interviewed?, as that one deals with the case where the candidate had other interviews and it is about graduate school admissions, while mine is related to a later career stage. In addition, as there is an academic component in the situation, I preferred to ask the question here instead of Workplace SE.
Any thoughts would be welcome.
1 What I mean by R&amp;D positions are those positions where you work in the context of EU R&amp;D projects. I hope that's not too vague as a definition.
Short answer: Yes, you should answer honestly.

Long answer: your question contains, implicitly and explicitly, several (mostly) flawed premises.

Premise 1: professors are superficial people who can’t be bothered to come up with their own idea of how good you are as an applicant based on the strength of your application, so will resort to relying on an (essentially) irrelevant piece of information to guide their decision.

The reality: almost no professor would care whether you have an interview elsewhere, or, to the small extent that they might care, it’s mainly to help them figure out if there’s any time pressure to reaching a decision on your application. In the case of truly stellar applicants the knowledge of other pending interviews/offers may affect the salary the professor might offer, but in normal cases it won’t.
There’s also a small number of professors for whom the assumption you’re making may be valid. But by and large the premise is not an accurate description of reality.

Premise 2: you are as good of a liar as you think you are.

The reality: you aren’t. In your question you only factor in the perceived cost of acting honestly (and are incorrect in how high you think that cost is, see premise 1 above) but completely ignore the very real - almost certain in my opinion - possibility that the alternative approach of trying to make yourself look much more desired than you are by not telling the honest truth would come across as clumsy and clueless in the best case, or shady and dishonest in the worst case. That eventuality will lead to a much worse outcome (certain rejection of your application, and a bad reputation that could follow you far into the future) than the eventuality you are actually expressing concern about.

Premise 3: if you say you don’t have any interviews you will have to accept an offer very fast since “they know [you] don’t have other options”, even if in the meantime you do receive some other offer.

The reality: this is false. You seem to have the misguided notion that by stating you don’t currently have other interviews you are committing yourself to never having any interviews. That’s not how the world (academia or anywhere else) works.
Hope this helps, and good luck with your interview!