Orchestrator-workers on Twelve HTTP status codes, by the book

All 12 codes are defined in RFC 9110 (HTTP Semantics), which replaces RFC 7231. Three workers checked the codes against https://www.rfc-editor.org/rfc/rfc9110.html. Their reports agree with each other, and each code's own section agrees with the summary list in Section 15.1. They did not compare against the httpwg.org copy. I had no tools myself, so this answer relies entirely on their reports.

Which codes are heuristically cacheable

Section 15.1 settles this. It says: "Responses with status codes that are defined as heuristically cacheable (e.g., 200, 203, 204, 206, 300, 301, 308, 404, 405, 410, 414, and 501 in this specification) can be reused by a cache with heuristic expiration unless otherwise indicated by the method definition or explicit cache controls [CACHING]; all other status codes are not heuristically cacheable." (https://www.rfc-editor.org/rfc/rfc9110.html)

• Heuristically cacheable: 203, 206, 308, 405, 410, 414 and 501. Each one's own section also says so, e.g. "A 308 response is heuristically cacheable; …" (https://www.rfc-editor.org/rfc/rfc9110.html)
• Not heuristically cacheable: 303, 307, 413, 421 and 422. None is in the list, and their own sections say nothing about it.

Reason phrases RFC 9110 changed

• 413 is now "Content Too Large"; older specs called it "Payload Too Large".
• 422 is now "Unprocessable Content"; RFC 4918 called it "Unprocessable Entity".
• 421 (from RFC 7540) and 422 are now defined in RFC 9110 itself.

Summary by code

Each quote in the JSON below comes from that code's own numbered section, as the workers read it with fetch_page.

{"answers":[
{"code":"203","reason":"Non-Authoritative Information","section":"15.3.4","heuristicallyCacheable":true,"quote":"This status code allows the proxy to notify recipients when a transformation has been applied, since that knowledge might impact later decisions regarding the content.","url":"https://www.rfc-editor.org/rfc/rfc9110.html"},
{"code":"206","reason":"Partial Content","section":"15.3.7","heuristicallyCacheable":true,"quote":"The 206 (Partial Content) status code indicates that the server is successfully fulfilling a range request for the target resource by transferring one or more parts of the selected representation.","url":"https://www.rfc-editor.org/rfc/rfc9110.html"},
{"code":"303","reason":"See Other","section":"15.4.4","heuristicallyCacheable":false,"quote":"This status code is applicable to any HTTP method.","url":"https://www.rfc-editor.org/rfc/rfc9110.html"},
{"code":"307","reason":"Temporary Redirect","section":"15.4.8","heuristicallyCacheable":false,"quote":"Since the redirection can change over time, the client ought to continue using the original target URI for future requests.","url":"https://www.rfc-editor.org/rfc/rfc9110.html"},
{"code":"308","reason":"Permanent Redirect","section":"15.4.9","heuristicallyCacheable":true,"quote":"A 308 response is heuristically cacheable; i.e., unless otherwise indicated by the method definition or explicit cache controls (see Section 4.2.2 of [CACHING]).","url":"https://www.rfc-editor.org/rfc/rfc9110.html"},
{"code":"405","reason":"Method Not Allowed","section":"15.5.6","heuristicallyCacheable":true,"quote":"The origin server MUST generate an Allow header field in a 405 response containing a list of the target resource's currently supported methods.","url":"https://www.rfc-editor.org/rfc/rfc9110.html"},
{"code":"410","reason":"Gone","section":"15.5.11","heuristicallyCacheable":true,"quote":"The 410 (Gone) status code indicates that access to the target resource is no longer available at the origin server and that this condition is likely to be permanent.","url":"https://www.rfc-editor.org/rfc/rfc9110.html"},
{"code":"413","reason":"Content Too Large","section":"15.5.14","heuristicallyCacheable":false,"quote":"The 413 (Content Too Large) status code indicates that the server is refusing to process a request because the request content is larger than the server is willing or able to process.","url":"https://www.rfc-editor.org/rfc/rfc9110.html"},
{"code":"414","reason":"URI Too Long","section":"15.5.15","heuristicallyCacheable":true,"quote":"The 414 (URI Too Long) status code indicates that the server is refusing to service the request because the target URI is longer than the server is willing to interpret.","url":"https://www.rfc-editor.org/rfc/rfc9110.html"},
{"code":"421","reason":"Misdirected Request","section":"15.5.20","heuristicallyCacheable":false,"quote":"A proxy MUST NOT generate a 421 response.","url":"https://www.rfc-editor.org/rfc/rfc9110.html"},
{"code":"422","reason":"Unprocessable Content","section":"15.5.21","heuristicallyCacheable":false,"quote":"For example, this status code can be sent if an XML request content contains well-formed (i.e., syntactically correct), but semantically erroneous XML instructions.","url":"https://www.rfc-editor.org/rfc/rfc9110.html"},
{"code":"501","reason":"Not Implemented","section":"15.6.2","heuristicallyCacheable":true,"quote":"This is the appropriate response when the server does not recognize the request method and is not capable of supporting it for any resource.","url":"https://www.rfc-editor.org/rfc/rfc9110.html"}
]}