How many songs is the average person familiar with?

I used to know lyrics and chords or notes for over 100 songs.

Answer to your question hundreds and hundreds !

Hundreds

Hundreds, maybe thousands.

And if you add in classical music, hundreds more.

I have 4000+ songs on my phone and that isn’t all the songs I am familiar with. It’s just the songs I had on CD that I converted over. There are probably thousands more I am familiar with.

As a Septuagenarian, I have a minefield of songs available for recall. My computer holds over 10K of songs that hold a specific meaning for a special time in my life. Can I start singing them word for word on demand??? Probably not. Still, when they start to play, I know every word!!! Some of them I recognize from the very first chord. The 60s & 70s were a very special time for connecting with music.

Now, the average person isn’t as deeply involved with their music, so I’d guess hundreds of songs for the average listener.

There really is no way to determine this. The average person may listen to over a million songs. Yet the average retention ability of a person can vary based on many variables. It also varies based on their age.
Even for myself who listens to a huge amount of music since I was young and my retention is better than most as a musician, I have no way to test or measure this.

^^As a Septuagenarian musician, I think I know thousands in different genres. There are “folk songs” I’ve known since I was five, I still remember my first French horn solo, “Panis Angelicus” which I learned over 60 years ago. More recently, I love “Tennessee Whiskey!” but can’t drink it anymore!