Exchange Routing Problem - Edge server with scoped connector

[Urs01]

We have 2 Exchange Server 2016 in AD-Site A with a send connector to the internet (not scoped) with adress space *
We have 2 Exchange Server 2019 in AD-Site B with 2 Edge Servers. We have a created a send connector with the edge subscrition. Afterwards I have configured this connector for SMTP Domains (contoso.com) and marked as scoped.
When I send an email in site A to contoso.com the message get routed over the scoped connector in Site B. 
In my opinin the mail should be routed over the send connector in Site B.
Connector selection in external message routing | Microsoft Learn
Did I miss something?

[#2]

@Urs01 

Check the priorities of your connectors!
Connector priority determines the order in which connectors are used to route messages.

[#3]

I can't see any priorities, do you mean the cost value on the addressspace on the connector?

[#4]

Below view command.
AddressSpaces is value "1","2".

[PS] C:\Windows\system32>Get-SendConnector

Identity AddressSpaces Enabled
-------- ------------- -------
SMTP {SMTP:*;1} True
contoso.local {SMTP:contoso.local;2} True

[#5]

@TAE_YOUN_ANN 

It didn't help. Exchange always seems to take the most specific send connector and doesn't take into account cost or "scoped send connector"

[#6 · Accepted solution]

@Urs01 

By design, this is the intended behavior.
When selecting a Send connector, Exchange always prefers the most specific (scoped to a specific domain) Send connector.
This is due to Exchange's routing behavior, where scoped Send connectors are given higher priority.

[#7]

Many thanks for your help.
I could not find any documentation that Exchange chooses the most specific send connector and does not care about scoped send connectors (AD-Site)