I am in engineering too and travel all over NA for work, where I spend a day in office or casual dinner meetings the a day or two in the field measuring workshops and large crew equipment while wearing a vest and steel toes.
Fyi. Texas esp Houston but also Dallas was dressier in office than most other places in NA. You can tell by all the dress choices in the stores, selection is 10x what I find elsewhere.
Summer weight office dress, not short, with cap sleeves and a bit float is A good choice. Something with pattern or darker that does not show wrinkles, and loose fit because of the climate. And poly blends are more office than anything cotton and beachy.
My go to packing includes brown cotton pants from banana republic, paired with a very new collared polo shirt, cotton short sleeve blouse like you showed, And a dressier top. Ballet flats, steel toes, And something to go for walks in. The dressier top and dark pants and a necklace or scarf makes people forget you are a bit more casual on the bottom, is easy to pack. I find you sit mostly when you need to wear this.
Men don't have the same footwear dilemmas we do so always pack a pair of walking shoes that look ok with your outfit. Men will say things like 'let's walk the 2 miles to the restaurant (in Houston)'. My ballet flats are actually north face from thrift store. I can walk a few miles in them for sure!
Pack a longer office dress or skirt that you don't need to wear pantyhose with, that is cool, but could go to church with your grandma. Lol. For Texas only.
Bring a light summer weight sweater for the plane and a/c that fits in oversize purse. Or short sleeve blazer that looks ok with jeans or slacks. Don't wear jeans tho
I bring a second pair of 'crawl on the dusty ground' slacks for my fieldwork, and I don't usually bring a dress because of there being no room for another pair of shoes, unless in full day meetings in corporate office justifies checking a bag.
Dark slack hide dirt and wrinkles while travelling, too.
I hope this helps.
( now ask me about Edmonton at -30!).