Mail not sending

That is two very different problems.

S/MIME is encrypted email which uses a certificate which is checked against a Certificate Authority CA server. If it cannot reach the server or the certificate is expired, you will see such errors.

As to Gmail, if you enabled MFA / 2FA Multi-factor or 2-Factor Authentication) then you will need to go to the Google accounts and Security web page and create an App Password for Apple Mail to use. This password will be different from your primary password. Go to myaccount.google.com and sign-in and click on Security and if 2-Step Verification is turned on. You may need to click App Passwords and create a password for your email access.

Check your Mail accounts screen and verify the Google account is your account and not your wife's account. But I suspect the suggested login info was coming from your Keychain which saves passwords and it was attempting to provide the wife's account.

Since it's related to sending email. It is possible the person you are sending to has an expired S/MIME certificate that you previously saved. They can be used to validate an email as legit or to fully encrypt the email. For S/MIME signed email you accept their public certificate which needs to be checked against a Certificate Authority CA. That is what the error is failing on. So it might be the person to whom you are corresponding or it might be your own public/private key certificate.

In order to exchange encrypted email with another individual using S/MIME you both need to have private key certificates and you share your public key certificates with each other. The certificates are used to automatically decrypt the email. If someone gained a copy of the email without the required certificates they cannot read the email, it's scrambled.

For the second problem. Go to Mail -> Settings -> Accounts and disable the Gmail account by unchecking the box on Enable this Account. Then add the Gmail account and see that fixes the problem. If it does you can remove the disabled account.

google/gmail may need you to login manually via a web-browser,

to inform you some changes they have done,

or to ask/verify your account by communicating with you directly,

so pls do so ...

make sure your gmail account is in good working order/condition.

( provide them info on what they ask from you )

then proceed to next stage, in apple Mail (or in Thunderbird).

find the IMAP & SMTP server setup detail settings, make sure the "OAuth2" is selected & mentioned there, next to "Authentication Method".

click/tap on gmail Inbox.

if apple-Mail opens-up a small web-page from GMail, & ask you to approve the apple-Mail email-client for OAuth2 based authentication login, then select "Allow".

to me, it appears, one of your your SMIME cert's validity has expired,

it could be the SMIME CA Cert, or it could be the SMIME client cert that was assigned for you.

Either you or family members, or one of your office admin has setup it for you,

so that Encrypted comm/emails in between you & office person's email, remains encrypted with SMIME.

Even if you setup SMIME, users who do not have matching SMIME, you can still comunciate with them via non-SMIME (non-encrypted email).

And, if you use email-client Thunderbird (TB, )then you can still use OpenPGP based encryption.

In apple Mail, when you setup GMail for 1st time, then it opened up a new web-window with a google GMail's specific URL webpage, at that moment GMail user needed to approve that OAuth2 based authentication (and press "Allow" button/key),

once user approves the apple Mail (or other email-client), from then on, OAuth2 based authentication will work fine in email-client, (specific app password is not necessary, but can be a plus).

Kindly use Thunderbird in Ventura.

Ventura's apple-Mail all bugs are not fixed yet.

Keep on monitoring/check if apple-Mail's bugs are fixed or not, but in the mean time use Thunderbird.

export SMIME CA cert & SMIME cleint cert from apple Mail, & import into Thunderbird, for the gmail account.

even w/o SMIME cert in TB, you can send emails to your office mates & to your wife, but BE AWARE, THOSE WILL NOT BE ENCRYPTED ANYMORE, with old SMIME cert anymore.

And if you reply to your old office/business person's email, who used the SMIME encryption protection,

then you have to be careful,

their old email's content if visible then SMIME decryption working, so you can reply with SMIME encryption.

But if old email's content is not visible then SIMIME is not working then do not include their email's old content back as a non-encrypted email, as thats not what they or you want, no one wants to create loss of privacy or loss of confidentiality.

gmail rolled out OAuth2 usage, some users were allowed to use older methods, for longer time, but at some point of time, they will not support older login anymore, i gues, that could be one reason, when your email was not working anymore.