Adding social media icons to email signature apple mail with url or SVG, not by attachment
So, to my knowledge SVG isn't possible in HTML email. As I understand it you have to create a placeholder signature and then find the .mailsignature file in your system. This will be in the iCloud folder on more recent systems and in the Library folder on older systems. From there you should be able to replace the <body></body> tags in the signature file leave the header as is. The process is a little more complex, as you'll have to make sure your signatures aren't using the default font and that you configure your text editor to open as unformatted HTML. There's nuances to the process, but there should be no reason you couldn't use an URL for an image. They will get treated as attachments unfortunately regardless of how you add it I believe, and you can't really do much about how the signature looks past the first time it is delivered. Good luck and I hope this helps.
You can add HTML img tags (linking to your social images) by manually editing your Mail.app email signature files. These will NOT show as an attachment on the recipient's email. Of course these will only work if the recipient's email client loads remote images.
Signature Location
The .mailsignature files will be in one of two locations depending on whether or not the email using the signature is an iCloud account.
If the account is an iCloud account, the .mailsignature files can be found here:
~/Library/Mobile Documents/com~apple~mail/Data/MailData/Signatures/
If the account is not iCloud, the .mailsignature files can be found here:
~/Library/Mail/<Vx>/MailData/Signatures/ (where <Vx> is a version dependent on your current install, in Mojave mine is V6).
Editing .mailsignature Files
You may want to create a new signature (and associate it to your desired account). It will then show in these folders as the most recently modified .mailsignature.
Edit this file in a text editor that can view the HTML code (replace anything in the tags below the "Mime-version: ..." line).
For the simplest example, your file could look like:
Content-Transfer-Encoding: 7bit
Content-Type: text/html;
charset=us-ascii
Message-Id: <C29....>
Mime-Version: 1.0 (Mac OS X Mail 12.4 \(3445.104.11\))
<body><img src="http://www.example.com/remote_image.jpg" /></body>
Important Note for non-iCloud Accounts
If you're not using an iCloud email account, you MUST lock the .mailsignature files after editing, or they will be overridden.
Using the .mailsignature Files
Once you've edited the .mailsignature file, quit Mail and reopen. You can now select the .mailsignature you edited.
NOTE: Images from tags will not appear in either the compose window or in the Signatures tab of Mail preferences, but they WILL appear in messages you send (if the recipient loads remote images).