I’m a recent new user of Sublime Text. But since you had no reply and I’m curious to learn more (and also on Ubuntu) I ran subl --help to see command line options available.
https://www.sublimetext.com/docs/commands
It seems that you can open a project using subl --project
and the window size should be remembered according to what I read.
Another approach I tried as an experiment (on Ubuntu) was to use GUI Actionaz for automation (it is in the Ubuntu Software Centre or look in Synaptic Package Manager … but is available for Windows users).
https://wiki.actiona.tools/doku.php?id=en:start
By writing System > Command you can call subl to open a project.
if you wish you can add further automation actions by referring to the shortcuts in Sublime toolbar
e.g. New File is Ctrl+N.
I guess you could refine automation script by adding Sublime commands.
Each command may take one or more parameters, which may be enclosed in quotes. For example, the command to insert the string Hello World!, followed by a newline, is:
insertCharacters “Hello World!\n”
{Later edit]
I found this thread which is relevant …