SRT is a sidecar file. Basically, it's a small text file with no formatting other than which lines of text have to appear when.
So you cannot specify the font or size with this type of file. The player determines which font is used and how large it is displayed.
If you want more control over your subs, I'd suggest you bake in the titles or use another form of subtitling (which is not as widely supported on social media). You can read more here: https://www.quora.com/Can-you-edit-font-colour-position-in-an-srt-file...
There are many types of subtitle files, and even in srt, there are optional codes for formatting. And PR will export some of those in a "styled" srt. BUT, as Richard says, it is then up to the player's options as to whether it will read those codes, ignore them, or let the user decide.
When using Subtitles (the previous version Open Captions), you have two choices for sidecar export, srt or stl (EBU N19). But, so far, you can only export stl when exporting media, not from the Text Panel.
I just did a quick test, making changes in font size, font color, stroke size and color, screen position, and background styling. I tried both "Open Subtitling" and "Teletext Level 1" as the code standard. VLC used the stl file as a caption track without my selecting it.
Open Subtitling gave better results. VLC only used the font color, stroke (not sure about size or color). Background varied, but I could not tell that it was my changes it was tracking. It ignored font family and positioning.
Results could be different if I used other export settings in PR, or if I used different settings in VLC.