In Thunderbird I see two methods of accessing/editing SMTP settings for email accounts. 1. Using the "Outgoing Server (SMTP)" which displays all the email accounts in a list. You then select one and click "Edit" to view or edit it.

The canonical list of available SMTP servers)

2. On each email account page there is an "Edit SMTP server" button. Click that to view or edit the SMTP settings for that account.

Which opens the SMTP server associated with that identity in Outgoing server (SMTP). Due to the way outgoing servers are actually associated with an identity, not an account, the same SMTP can be used for multiple identities. It is one of the reasons you will see almost every discussion in these forums about SMTP suggesting the use of unique SMTP names for each entry in outgoing server (SMTP) do you know which is associated with when Identity.

I'm seeing two problems:

1 - The settings made using #1 above don't carry over into what I see using #2 above.

Yet the outgoing server (SMTP) is the canonical list from which the SMTPs you can choose for an identity is populated.

2 - Using method #2 above, changing the SMTP settings for my newest email account also changes the settings (seen using #2 above) on one other email account. And vice-versa.

As I said above. Change the names so each is unique and then you can stop using the same SMTP entry on multiple accounts and all the apparent issues will go away.

What could be causing this?

I think I have provided the reason. Duplication and non unique names for outgoing servers

I'm not clear what you mean by "names". Is that the same as the "Description" I see for each SMTP account?

If so, I gave each of those two SMTP accounts unique Descriptions.

Yes, names are the descriptions, Think of the SMTP pane as the list of available SMTP servers, and the account pane is merely pointing to one of the entries in the list. If you find that changing an SMTP entry for one account causes it to 'appear' to also change another account, that is indicating that you are using two accounts for one SMTP server setting - which will cause errors when sending a message.