I think https://dnncommunity.org/...-of-redirects-in-DNN might be helpful

I've read that article before I decided to ask here. All of those are for redirecting rather than rewriting. I am not 100% sure but I do believe the rules I have are correct, as before I had them "project/N" was not going to "project/id/N". I am missing something.

Have you tried running the regex through any validators to be sure you have the correct regex?  (I don't have the time to check it myself at the moment.)

https://regex101.com/

Yes, I ran it through the IIS regex testing tool. I also just ran it in regex101.com The regex seems to be working okay.

I'm not following your description of your idea. You seem to be wanting to redirect from A to B then rewrite from B back to A, but these are both in your inbound rules. Do you mean that you want DNN to natively process urls of the form "project?id=N", but accept urls of the form "project/N" and present links back to the end user in the form "project/N" ? If so, you'll need to set outbound rules.

Yes, the idea is for the user to see only "project/N", but for the server to process that as "project?id=N" so I can get the id parameter. Could you please explain why I need outbound rules and what they need to do? Or maybe direct me to an article that I could read about this? Thank you.

Sorry for delay replying - I'm short of time and have not tested, but I think you need something like the code below. You shouldn't need to redirect, just rewrite the url on the way in to the server. When the server generates its response you need to change urls back to the format you want the user to see by using outbound rewrite rules.

<rewrite>
<rules>
<rule name="projectin" stopProcessing="true">
<match url="/project/([0-9]+)" />
<action type="Rewrite" url="/project?id={R:1}" />
</rule>
</rules>
<outboundRules>
<rule name="projectout" preCondition="IsHTML" stopProcessing="true">
<match pattern="/project\?id=([0-9]+)" />
<action type="Rewrite" value="/project/{R:1}" />
</rule>
<preConditions>
<preCondition name="IsHTML">
<add input="{RESPONSE_CONTENT_TYPE}" pattern="^text/html" />
</preCondition>
</preConditions>
</outboundRules>
</rewrite>

Thanks for the response! However, this still doesn't fix my issue.

Scrap the outbound rule - this is not the part I need help with. The problem I need fixing is that when the user requests a page with the format "project/N" he gets redirected to "project/id/N". I don't know where that redirect comes from, but I want to stop it.

It happens only when the inbound rule for the rewrite is active. I tried your rule and mine (I had to remove the / at the start from your for it to work) and both have the same result.

Please let me know if you have any other suggestions.

I'm not sure I understand the issue correctly, but to me this seems as if DNN is rewriting the url for you.
Did you add an exception for the rewriting to SEO > Expressions > Ignore URL Regular Expression?