I have found the answer here:
https://thesmsworks.co.uk/blog/emojis-sms/
Using an emoji will require the whole text message to be sent in unicode. Unicode is an encoding standard that allows you to send characters that are not part of the standard character set that you would normally use. (The standard characters are known as the GSM character set.)
When sending a text in unicode you have fewer characters per text credit to play with.
A standard text allows you to send 160 characters per text credit. When you send an emoji (and send using unicode), this is reduced to just 70 characters.
So emojis are sent as Unicode, but the overall message allowance reduces by the conversion of the whole message from ASCII to Unicode.
Re-addressing my previous calculation:
160 x 2 - 111 = 209
to
70 x 3 - 4 = 206
...so the emoji occupied -3 units (whatever the current unit is). Something is not quite right, but it's close.
What's the correspondence between 160 plain characters and 70 Unicode characters?
Maybe 160 x 7 bits = 70 x 16 bits.
But surely that's not the whole answer, because there might be some preamble to tell the receiving end that it's Unicode, and not all Unicode is 16 bits. As I understand it, Unicode is a superset of ASCII, so wouldn't the plain characters correspond 1:1 in Unicode anyway? Maybe, instead of "Unicode", we should be talking about UTF-16.