Circular and Non Rectangular
While these displays might technically fall under the more traditional display types, non-rectangular displays do feel like a bit of a special beast that warrant their own category. Even 1x1 square displays, while rectangular, are still a bit hard to find these days.
Circular Displays
There aren't a ton of specific providers for these displays for consumer use since the cost and difficulty to produce makes them less likely to be produced in small volumes.
Here are a couple resources I've come across for round and rounded edge displays:
Waveshare has a number of circular displays at sizes from around 1" to 5" diameter (with a square resolution). Surprisingly reasonable prices of less than $200/unit and just regular HDMI input drivers. They also have a couple displays with rounded edges instead of corners at various small sizes as well. As a bonus, most of these also include touch sensing capabilities as well. I currently see resolution ranges at around 240x240 for the smaller ones and 1080x1080 for the larger ones.
Adafruit also has a a couple circular displays meant to be combined with things like Raspberry Pi's
Crystal Display Solutions has a range of options for circular as well but no specs on size ranges.
Some of these smaller displays are not necessarily meant to be driven by an HDMI connection and might need something a little more exotic like an SPI or ribbon connector to a driver.
SInce the use case for these displays is rare, usually the circular effect is achieved by putting a physical mask overtop of a standard display.
Non-Rectangular
These are a bit more unusual than circular displays. The only ones I've seen very occasionally are triangular displays, but they aren't produced very often.
Here is one resource I've seen for a Triangular display
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