Is there a word, or maybe an expression, to when someone is walking towards you, and you both stop, and doesn't know who should go to the left or right to keep walking?

Logicians call situations like this a deadlock. There is also a livelock where both of you step to one side and back but synchronized so that you continue to block each other. Informally I’ve heard it called a Mexican Stand off. But there is no common English word.

I would call that a Zax standoff (referencing the book by Dr. Seuss), but I don't know of a standard or common word or phrase for it. A related phrase is "playing chicken", but that's more a situation where people are deliberately heading straight toward each other (possibly in some sort of vehicles) and trying not to be the one to "chicken out" and swerve to avoid the collision, rather than a mere awkward passing.

I call this Tuesday (or literally any day of the week) lol. If there truly is a word for this, I do not know it, but I experience it quite frequently.

Mexican standoff

I've heard it called an awkward dance but that's not very poetic. Some people might joke "do you want to lead or should I?"

Not widely recognised, but: https://youtu.be/GmeXE8KM0VA

I say thanks for the dance

Op excuse me sorry haha ha have a good day

No, there really isn’t. “I almost ran into someone today. Literally.” “I literally almost ran into someone.” If you had bumped into them (we usually just say ‘ran into’) then the *almost* is dropped.

I call it a "Canadian stand-off". It's not a real phrase, but it's served me well over the years.

I call this the hallway dance

Not really. You could say you both stopped short and tried to figure out how to get around each other.

I think there's a Scots term, but of course I dont remember what it actually is. If I'm remembering correctly, I heard it on the Who Knew It podcast. I'll do a bit of research and come back.

I think it was Peter Kay who did a bit on his comedy show on this, he just referred to it as dancing 😂 it's funnier when he says it, obviously.

I'd say there's no simple term or idiomatic phrase for this that is universal enough to count on.

Oh-uh-mm-ah usually covers it

Impasse maybe?

a dance.

My friend group has always just called it "the dancey dance"

In the Midwest, you just say "ope" and move along with your day.

There is a fun book entitled "The Meaning of Liff", by Douglas Adams. The dude who wrote The Hitchhiker's Guide to the Galaxy". It uses placenames for new words; (Note, these are not real words. Just fun.) --- CORRIEARKLET The moment at which two people, approaching from opposite ends of a long passageway, recognize each other and immediately pretend they haven’t. This is to avoid the ghastly embarrassment of having to continue recognising each other the whole length of the corridor. CORRIECRAVIE To avert the horrors of corrievorrie, corriecravie is usually employed. This is the cowardly but highly skilled process by which both protagonists continue to approach while keeping up the pretence that they haven’t noticed each other–by staring furiously at their feet, grimacing into a notebook, or studying the walls closely as if in a mood of deep irritation. CORRIEDOO The crucial moment of false recognition in a long passageway encounter. Though both people are perfectly well aware that the other is approaching, they must eventually pretend sudden recognition. They now look up with a glassy smile, as if having spotted each other for the first time, (and are particularly delighted to have done so) shouting out ‘Haaaaalllllooo!’ as if to say ‘Good grief!! You!! Here!! Of all people! Well I never. Coo. Stamp me vitals, etc.’ CORRIEMOILLIE The dreadful sinking sensation in a long passageway encounter when both protagonists immediately realize they have plumped for the corriedoo much too early as they are still a good thirty yards apart. They were embarrassed by the pretence of corriecravie and decided to make use of the corriedoo because they felt silly. This was a mistake as corrievorrie will make them seem far sillier. CORRIEVORRIE Corridor etiquette demands that once a corriedoo has been declared, corrievorrie must be employed. Both protagonists must now embellish their approach with an embarrassing combination of waving, grinning, making idiot faces, doing pirate impressions, and waggling the head from side to side while holding the other person’s eyes as the smile drips off their face, until, with great relief, they pass each other. CORRIEMUCHLOCH Word describing the kind of person who can make a complete mess of a simple job like walking down a corridor.