This is amazing, fun and educational in one package! Thank you! Sorry this post got very long ;-)

Having difficulty settings like

* tourist

main streets / squares, maybe some (renowned - although that might take some additional Wikipedia/Wikidata data sources :-))
landmarks if those can easily enough be extracted from OSM data

easter egg mode for s/Paris/your favourite City with underground transportation/: find a specific metro station :-) (any entrance would count)

* resident

"tourist" + smaller streets + any street really close to the circle center (15 minutes by foot / 5 minutes by car
-- oh, you'll just have to add flooding algorithm :-) ^^)

* pedestrian

"resident" + smaller streets everywhere but with greater probability closer to the circle center + footpaths
(although with them probably lacking proper names most of the time that could be hard - but you could include
e.g. streets from pedestrian zones)

* taxi driver

everything ^^

would be great :-)

And then there could be (best optional) penalty modes, too:

* "resident"+:

if you pin a street that is more or less orthogonal to the target street
(say their mean directions intersect at more than 45 degrees ; and the pin is sufficiently
far away (30m / 10% of map height / half a block?) from their intersection (if any exists)
to rule out precision errors) you get only 1/2 the points

* "resident":

if you pin a street the wrong direction off a main street (and the target street
does not cross the main street) you get only 2/3 the points
(i.e. main streets intersecting the plane and you picked the wrong "half")

"tourist":

the same but for cities with rivers where you picked the wrong bank

I also found the circle a bit big for my taste/confidence and cheated a bit by not placing the circle center at my location but so that I would still get my neighborhood but more of the outskirts than the city center...

I also got very lucky with the streets, so got 330/500 on my first try.
One was certainly also due to a square that is also used (at some specific times) for car traffic.

As an interesting effect, I got the first street wrong by some meters (and orientation :-\) and the 5th street was the same street again.
At first I was a bit puzzled, and then got full marks for that one :-)
I saw that you got the report of repeating streets already in some other comment already but that experience led me to another idea:

It would be a great learning aid to (optionally) go through the (widely?) missed streets again after the 5 rounds.

And if we could even re-claim some (small) amount of points for getting them right the second time that would certainly help our brains etch in the correct position even more :-)

A small aside: I found it pleasantly devious that the circle restricts the scrolling at higher zoom levels! Just in the cases where the target street is very close to the border it might be nice to relax it a bit though...

And while trying it out on Desktop I discovered a possible bug:

While choosing the location, when pressing the "Zoom In" button 2-4 times suddenly street names were displayed again!
Is this intentional so people can easier find their starting point?
Firefox 98.0 on Linux

My last point:

Would it be possible to export a map view to print it out in good quality for offline reconnaissance / tinkering?