Is there a way to see what time a message was sent? There are many websites that incorrectly claim that you can do this by swiping left and holding within the Messages app, but this actually shows the times that the messages were received, not sent.
I'm talking about a situation in which the sender or recipient doesn't have reception, the recipient's phone is off, etc. The Android Messages app shows both sending and receipt time, which I find very handy.
Is there a way to see on an iPhone what time a message that I received was sent?
Generally, no.
The only easy source of send times is visual inspection on the sending device.
Forensic analysis of the message database would be needed to get more precision or data that is not displayed by the iOS app.

https://blog.elcomsoft.com/2020/10/the-forensic-view-of-imessage-security/

There will be server logs in some cases (SMS being less secure / more logged than Apple as a carrier using iCloud and your AppleID for delivery) as well, but on the receiving device you will likely need to jailbreak it and dig into the database and log files.