I'm no Python expert at all, but it looks like user and password are missing. (uid and pwd??)

From the error you get I suspect you are sending your HS.Message.PatientFetchRequestAsync to the wrong service/endpoint in the remote server.

How are you sending your request and how the operation is configured?

The first parameter (Lookup Table Name) of Exists function must be quoted: Exists("HologicProcedureFilter",.....)

If you want, you can switch to the old zen based rule editor, in the upper right of the page click on the user icon and select Open in Zen rule editor:

Note that it will open the rule in new tab, leaving the old tab open, make sure you use only one tab to edit the rule!

Assuming response1 json ALWAYS contain a single entry, then:

    ; import stream into Dynamic Object
    Set Response1=##class(%DynamicObject).%FromJSON(response1.informesAutorizadosRangoFechas)
    Set Response2=##class(%DynamicObject).%FromJSON(response2.informesAutorizadosRangoFechas)
    
    Write "Response1 has ",Response1.entry.%Size()," entries",!
    Write "Response2 has ",Response2.entry.%Size()," entries",!

    ; loop all the entries in Response2
    Set EntryIter=Response2.entry.%GetIterator()
    While EntryIter.%GetNext(.EntryKey, .Entry) {
        Write "Response2, entry ",EntryKey+1," has ",Entry.resource.%Size()," resources",!

        ; loop all resources within Entry
        Set ResourceIter=Entry.resource.%GetIterator()
        While ResourceIter.%GetNext(.ResourceKey, .Resource) {

            ; add resource from Result2 in first entry of Result1
            Do Response1.entry.%Get(0).resource.%Push(Resource)  
        }   
    }
    Write "Merged Response1 has ",Response1.entry.%Get(0).resource.%Size()," resources",!

Using your samples the output is:

Response1 has 1 entries
Response2 has 7 entries
Response2, entry 1 has 1 resources
Response2, entry 2 has 1 resources
Response2, entry 3 has 1 resources
Response2, entry 4 has 1 resources
Response2, entry 5 has 1 resources
Response2, entry 6 has 1 resources
Response2, entry 7 has 1 resources
Merged Response1 has 8 resources

The resulting json is different than your manual merge.......

We had this same issue (missing support for SNI) long time ago, I think using healthshare based on cache version 2015.2.

I'm afraid you need to add this to the (possibly very long) list of good reasons to upgrade.

In %Stream.* classes setting the Filename property corresponds to calling the LinkToFile() method (see FilenameSet() method).
From LinkToFile() documentation:

The method as its name suggests creates a LINK to an EXISTING file.
....
Also note that if there is currently some temporary data in the old stream when the LinkToFile is called this temporary data will be removed before the stream is linked to this filename.

I think you have two options:

1. set Filename BEFORE writing to the stream
2. when you need to save a stream to a specific file, create a new file stream and use CopyFrom() method to copy existing data

For option 2 here is a sample (using %Stream.TmpBinary for the temporary stream):

set tStream = ##class(%Stream.TmpBinary).%New()
do tStream.Write("whatever stream contains")
set finalStream = ##class(%Stream.FileBinary).%New()
set finalStream.Filename="c:\temp\streamtest.txt"
do finalStream.CopyFrom(tStream)
write finalStream.%Save(),!