Getting these;
Undefined index: view in \components\com_content\helpers\legacyrouter.php on line 99

Fixed.

Please confirm that this is the expected behavior with different URLs to the same pages.

Link in the Archived Articles module.
http://localhost/joomla-cms-staging/en/archived-articles/2011/1
pagination: http://localhost/joomla-cms-staging/en/archived-articles/2011/1?start=5

Using the archive filter form:
http://localhost/joomla-cms-staging/en/archived-articles?month=1&year=2011&limitstart=0
http://localhost/joomla-cms-staging/en/archived-articles?month=1&year=2011&start=5

Currently yes. Staging has the same.
This happen after the second commit but the real problem is probably somewhere else.

I have tested this item ✅ successfully on 88122a0

I found a place in code where I can fix it but I won't add it to this PR.

This PR is ready to test.

Please provide an example for the last commit.

When SEF is ON go to page like index.php?option=com_content&view=archive&Itemid=256&lang=en&month=0 (adjust to your Itemid for index.php/en/archived-articles)

Then check URL for the page 2.
Before: index.php/en/archived-articles?month=0&start=5
After: index.php/en/archived-articles?start=5

At the moment, it's a bit pedantic, but when I fix below issue

Using the archive filter form:
http://localhost/joomla-cms-staging/en/archived-articles?month=1&year=2011&limitstart=0
http://localhost/joomla-cms-staging/en/archived-articles?month=1&year=2011&start=5

it will be more useful.

I still get this index.php/en/archived-articles?month=0&start=5 with/without the PR.

Please follow instruction.

The last commit hide parameter month=0 in a next page link when you are first time of non SEF URL.
The link is not SEF but your joomla has SEF enabled and limit field value 5 is saved in session.

1. Go to index.php/en/archived-articles and set limit to 5.
2. Next go to non SEF URL index.php?option=com_content&view=archive&Itemid=256&lang=en&month=0, which is equivalent of index.php/en/archived-articles.
3. Scroll to the bottom and check link for page 2:
   • before commit index.php/en/archived-articles?month=0&start=5
   • after commit index.php/en/archived-articles?start=5

Additional, if you apply below patch (I'm still working on it):

diff --git a/libraries/src/Router/SiteRouter.php b/libraries/src/Router/SiteRouter.php
index 6dbabc1ea0..35b5dfa881 100644
--- a/libraries/src/Router/SiteRouter.php
+++ b/libraries/src/Router/SiteRouter.php
@@ -404,6 +404,9 @@ class SiteRouter extends Router
                                        }
                                }
 
+                               // Set the information in the request
+                               $vars = array_merge($found->query, $vars);
+
                                $vars['Itemid'] = $found->id;
                                $vars['option'] = $found->component;
                        }
@@ -441,14 +444,6 @@ class SiteRouter extends Router
 
                        $route = implode('/', $segments);
                }
-               else
-               {
-                       // Set active menu item
-                       if ($item = $this->menu->getActive())
-                       {
-                               $vars = $item->query;
-                       }
-               }
 
                $uri->setPath($route);

then this will affect SEF links and after you click on filter you should never see parameters &month=0&year=0 on page links.

I have tested this item ✅ successfully on c15f303

I have tested this item ✅ successfully on c15f303

Ready to Commit after two successful tests.

It would be nice to add this PR to 3.8.4 milestone because this PR could be treated as regression.

Example:
index.php/en/archived-articles/2011 returns error 404 on staging but works in 3.8.3 and in this PR.

I'm wrong. I did not remember correctly the comment from #19397 (comment).

I did a simple test.

At 3.8.3:
Go to archive view (index.php/en/archived-articles) and set Month to Jan and limit to 5.
The filter, next go to the second page (index.php/en/archived-articles?month=1&year=0&start=5)
After that go to third page (index.php/en/archived-articles?month=1&year=0&start=10)
Success. You are on 3rd page.

At staging:
Go to archive view (index.php/en/archived-articles) and set Month to Jan and limit to 5.
The filter, next go to the second page (index.php/en/archived-articles/0/1?view=archive&start=5)
After that go to third page, it is broken (index.php/en/archived-articles?id=1&start=10)
Failed. You can not get to page 3.

At this PR:
Go to archive view (index.php/en/archived-articles) and set Month to Jan and limit to 5.
The filter, next go to the second page (index.php/en/archived-articles?month=1&year=0&start=5)
After that go to third page (index.php/en/archived-articles?month=1&year=0&start=10)
Success. You are on 3rd page.