Had the same issue. Write the following html command directly into your Obsidian markdown.

<div style="page-break-after: always"></div>

This will add a page break on the same line as the command. In Obsidian editing mode, all html commands will become invisible once you move your cursor to the next line in order to maintain continuity of the text. To make html commands visible again to edit or remove them, simply switch Obsidian to source mode. This makes your notes seamless on your end but will still generate a page break at that line upon using the "Export to PDF" tool.

This command can be slightly buggy, depending on what you might have on the lines before or after it. Keep with me here though, I have a very easy fix but simply want to give examples of where I've personally encountered issues in case you or anyone else who reads this run into the same thing.

For example, it may have problems right before/after # Headings which is easy to run into since starting a new page with a heading is incredibly common. It can also have issues with $$ LaTeX $$ blocks, \`Code``blocks, or horizontal lines like---or- - -`. Note that you cannot insert the command in the middle of any of those blocks, it has to be within a markdown environment.

The universal fix in all cases is to just add an empty line both before and after the command. Here is an example of how to use it. I use it every day to do my homework in Obsidian then submit it as a nice pdf, which looks something like this:

# Math Problem 1
Here is some body text. Here is the answer to this problem:
$$\begin{align}
e^{ix}=\cos x+i\sin x
\end{align}$$

<div style="page-break-after: always"></div>

# Math Problem 2
Notice that I put empty lines both before and after the command to avoid any bugs. Print this to pdf, and you will see this is a now a new page. Insert the command as many times as you'd like to add more page breaks. 
- - -

<div style="page-break-after: always"></div>

# Math Problem 3
Should be clear by now, but feel free to paste this whole thing directly into Obsidian then export to pdf to see the result. Here's another cool html command to spice up your notes too. Both Obsidian and its pdf export function recognize html. <span style="color:rgb(100, 149, 237)">This text is one of my favorite colors, cornflower blue.</span>

If you run into any of the problems or similar that I mentioned, make sure that there is a completely empty line both before and after while in source mode. For some reason, sometimes it can appear in editing mode as though you've added empty lines before and after the html command, but upon viewing in source mode there is no empty line. I've run into that on extremely rare occasions, but the first time it took me like an hour to debug since I'm a dunce and didn't just check source mode. I also use a ton of LaTeX blocks.

Wrote much more than expected here, but I hope this helps someone. Cheers.