I do have the a7iv + 200600G combo and like it. Please read a few comparisons between a7iii vs a7iv before you pull the trigger, if you haven’t already.
Sometime i have felt 200mm isn’t as wide as id like it to be when subjects are close by but have learned to let go of such moments with what the 600 can offer. A 100400GM with 1.4x can be a solution but the budget goes up significantly and can come with its set of challenges. if you are interested in birds, 200600G is the way forward.
with the season almost done, see if you can get any offseason deals. I’ve got my 200600G on Amazon for 1.5L. 200600G is highly rated and is a good match between performance and price.