Well I Google A 1005 and it is classified as travel tripod, meaning light weight. Aluminium construction at 1.45kg. folds to a short length.
Most important spec. is max. loaded weight and A1005 is 4 kg.
Now assuming using an A7iii at 650g including battery and 200 + 650 g Oss full frame telephoto lens at 2.1kg so total weight is 2.75 kg. When A1005 is 4kg. More than adequate right? In fact there is s used one at carousell for $80 with Y10 head. Seller has 2 but moving away so selling a spare. Do note this is an older series of product from Surui as they have latest series.
There is also a lighter class of tripod using carbon fibre but cost more and whether it is more stable or better depends on design but definitely lighter for travel or carrying for extended period of time.
That said I think it's better to spend and buy one time right than later need a more stable tripod
( heavier and cost more but it's relative to effective use. ) But the $80 pre-owned A1005 can play play.
A professional class tripod uses 30mm. diameter tubes for the biggest one and smaller ones to follow. Also the leg locking system is something to consider like quick open n snap type or screw twist lock which is more stable while the snap lock type will wear out and get loose as time go by. Plus maintenance and cleaning make twist lock more reliable.
Ok with that said, I would think a thicker 30mm. tube leg is the better choice so the A1006 ( not 30mm btw ) can take a 10kg. Load which is more than 2X the max. loaded weight of
A1005. Also take note that camera , lens setting and handling or how you hold or steady your setup also play a part in getting sharp photos.
Please take note the TX series do not come or include the tripod head , must buy separately!
Or you can choose Surui 2021 models like the TX series like T1024 carbon fibre 1Okg. or T2204 aluminium 12kg. Tube diameter 28mm. which is close to the 30mm pro types. Remember there are so many tripods in the market but Surui is cost effective from what they offer.
2021 Surui products, select English if you can't read Chinese.
Unfortunately birding has one of the highest requirements equipment (and budget correspondingly) wise. There's a reason why photographers lug their big lenses mounted on big tripods, as at high zoom any small movement results in camera shake and blurred photographs.
The Sirui tripod you found is their low end tripod, maybe can mount the Sony camera with 200-600mm to take the load off, but when quality is needed you probably have to consider something like those listed in this article:
What tripod can support a 600mm lens and still go on a long hike into the wilderness? We test out six higher-end, thick-legged, modular tripods that are comfortably tall and capable of supporting tremendous amounts of gear. This group review compares all six models, examining their features...
www.dpreview.com
As you can see Sirui is already on the lower end price wise but that's already >$500
Not to forget you also need a 'head' for the tripod, bird photographers will probably recommend getting a Fluid / Video head or Gimbal, and quality ones cost as much as the 'legs' or more.
I'll suggest you set your budget, get the best you can for that, then as the photographer gets more experience see what others are using and research what works best for him/her.