I'm trying to use ARIA Labels for accessibility by the way paragraph tag is working fine in chrome using narrator tool, but is not readable in Edge. I'm not using any aria attribute for this type of element; should I use it if I want to read the content?
<aside>
<img class="logo" title="bla" alt="Bla" src="logo.svg" tabindex="0" />
<h1 tabindex="0">Welcome</h1>
<p tabindex="0">blah bla blah</p>
<p tabindex="0" >bla blha</p>
<aside><!-- aside -->

I try to make a test with your above code in Edge with Narrator tool.
In my test, I can see that Narrator tool can read the text from paragraph and it also read the next paragraph when user press TAB key.
Below is my testing result.
I suggest you to start tabindex from 1 instead of 0 and check whether it may help or not.
I have a question that are you using the same code that you had posted above?
If not, Try to provide the exact sample code that you are testing on your side and also provide a detailed steps to produce the issue.
We will try to follow that steps and try to make a test again to produce the issue.