How to say "unsurprisingly" as in "Someone unsurprisingly did something"
果然 if we want to get all pedantic about this means, like you wrote, 'as expected'.
Oxford defines unsurprisingly as:

不足为奇地
unsurprisingly, she didn't show up
不出所料，她没有出现

Here we have two choices: (1)不足为奇, (2)不出所料...
and again defines unsurprising as:

不足为奇地
it is unsurprising that...
。。。不出预料

adding a third: (3) 不出预料
Like you mentioned at the beginning though 果然 would work just fine here...along with the three mentioned above (不足为奇, 不出所料, 不出预料) and a host of others:
果真
一如所料
果如所料
意料之中
take your pick...