You've all said exactly how to exclude welcome accounts from other flows or campaigns, but the really correct way is another.
Surely inserting a new property and deleting it at the end of the flow is the correct way, but have you ever thought that if a user enters the welcome series and the welcome filters are set, it will be all those who have not placed an order, from the moment the user will place an order before the end of the flow, will the ownership never be removed?
So my advice is to remove the property even if the user has made the first order, inserting the removal within the post-purchase flow.
What I'm saying always depends on how you set up the welcome series flow, for example for my ecommerce I don't want to send more welcome emails if the user buys and for this I had to insert a property removal both at the end of the welcome flow (if he does not purchase) the purchase trigger is triggered.
In this way we will have the possibility to communicate correctly with users once they leave the flow.