Improve type support, casting, and inference

[mathemancer]

Problem

Our current type-wrangling system is showing its age:

• Type inference is tied to casting
• Inference is therefore less powerful and slower than it should be
• Casting, on the other hand, is less flexible than it should be.

To solve this, we plan to make some major changes to the type-wrangling machinery in Mathesar.

Related, previously-existing issues

Some of these may or may not be actually implemented for this project, but I'm collecting everything ostensibly related here in one place for completeness and clarity.

• Column alteration should not require custom type casting functions. #402
• Mathesar should not depend on custom types being installed. #403
• Accept type_options when testing type casts, making it possible to test every type cast #869
• Explore short-circuiting for casting functions #957
• Handle human readable number casting in general #1309
• Add another number format when casting to Mathesar money type #1417
• Retain currency symbols from imported data for money columns #2169
• Make column type inference faster #2347
• Improve type inference tree #2371
• Move inference-related logic to Postgres #2372
• Make type-casting SQL functions parallelizable #2373
• Modify casting function names to avoid collisions #2820
• JSON string is castable to URI #2941
• Add hints/metadata for citext column type #2959
• Add hints/metadata for point column type #3007
• 500 when adding unique constraint on point column #3067
• Improve support for unknown types #3095
• Log SQL errors when altering fields #3111
• Database locale does not seem to be respected #3112
• Time Zones are inconsistent in Data Explorer #3184
• In our URI type, allow data entry of URLs without scheme #3408
• Improve typecasting in mathesar #3560
• Cast to date fails if date is in DD-MM-YY format #3953
• Couldn't cast a text column to money type #3954
• Restrict storing invalid URIs in a URI column #4188
• Couldn't cast "time stamp with time zone" to "Date" #4196
• Remove redundant casting functions #4333