Let me share my own experiences to start with.
Many a times, when I had to attend an interview, I carried notes with me as a rule. These were made while I was preparing for specific interviews. And as a habit I have always worked on making notes while preparing for interviews and resorted them for a quick brush-up just before attending one. I think I inculcated this habit during my school and college days while preparing for exams, where in I recall I made some good short and elaborate notes at times.
Coming back to the point of carrying notes into the job interview. Not all, but in a few interviews, I asked for permission very politely from the interviewer to refer to my notes at a certain point in time during the conversation, to answer a specific question. And that was a genuine ask, it was never forced or it never came about due to the fact that I had forgotten anything while answering to a question.
And let me tell you that I never noticed any element of surprise from the panel or the interviewer when I asked for polite permission. In fact, it was always the other way around. I observed a faint appreciation in the eyes of an interviewer or panel. But let me clarify, it was never about reading through the notes but just to refer them briefly to articulate my answers in a better way with the right amount of information. Also, it was not a frequent referral but once or twice at max during the conversation. In the later years as I began taking interviews and interacting with leadership teams/CEOs/Hiring Managers in the panel, they confirmed the following points on the subject:
“I feel making notes is a great investment made by potential candidates while preparing for an interview. It shows the level of seriousness of the candidates. It shows that the candidate is giving closer attention to things.”
“It shows the level of preparedness at the candidate’s end. It shows how important this job is for him/her. It is not just about notes, it is about the thought process, it is about the sincerity, it is about focusing on the right things.”
“It is quite nice to know that the potential candidate has taken the time out to make notes and to focus on things he/she believes would be important for the conversation.”
Let me also tell you that in my decades of hiring experience, very rarely I have seen an interviewer asked my permission to refer to notes, perhaps, I could just count on my fingers, the number of times a candidate would have asked me that. I strongly believe it is a cultural thing and specifically in an Indian context, carrying notes to the job interview would mean or could be perceived as “Unprepared”.
My personal opinion is not in line with this thought. An interview is a professional conversation. It is not a memory test or the test of mugging skills. It is not a school set up. It is perfectly fine to carry notes and ask for a permission to refer them once or twice, when genuinely needed.
Let us get a bit deeper into this.
What kind of notes are okay to carry and what are not?
You can not really carry everything in the form of notes into the interview conversation. It depends on the content of the notes that would decide if you can carry them with your or not.
The notes that can carry with you:

If you have jotted down the information about the organization while researching about them, you can carry it with you and refer them if required. This would include key facts about the organization, business health parameters, information about product and services or latest mergers and acquisitions or latest media coverage etc.

If you have prepared a list of questions you planned to ask the interviewer, as part of your notes, that is perfectly fine to carry with you in the conversation
Both these points mentioned above, would give a good indication to the interviewer that you have prepared sincerely and are thoughtful about it.
The notes that cannot carry with you:

If you have made notes on how you would answer a specific question or a verbatim of it, or about your work history or about your projects and highs and lows and lessons from it, you cannot carry it with you. Because you should be able to articulate your work history about key projects about your profile, about your experience confidently without referring to any of your notes. And for a moment lets assume you have more than 20 years of experience and you have done so many projects that it is hard to really recall all of them. In such cases, try to keep the focus on 2-3 big ticket items, the most complex or challenging projects undertaken by you and then successfully delivered.

The role of carrying notes is to bring some level of smoothness in the process and it enables the candidate to drive the conversation in a seamless manner. But there is something you should be very careful about. During a virtual interview on Zoom or Teams, when you have to refer to your notes, you will look down, the interviewer might be thinking that you are distracted or what is it that you are looking at, so it is better to inform the interviewer proactively that you will be referring notes in between. This would ensure that when you look down to read them, the interviewer is already aware of it.

Lastly, don’t forget that in the end it all boils down to how much meaningful investment of time has gone into your preparation for a specific interview. And notes are the resources candidates can certainly resort to, to drive a smooth and successful professional conversation.