2.5 year old keeps hurting her baby sister.

Not had my own children yet, but a teacher and seen this alot with older siblings, it sounds like your 2.5 yr old is jealous and hasn't been able to process having a baby sister. My advice would be never to leave them alone together for now, and make sure your older daughter gets special attention, on her own, from both you and your partner or ither family members.
You may find that play therapy or other approaches which allow for the child to process and come to term with the change and the new expectations are helpful, family support should be able to tell you what's available in your Local authority, if not SENDIASS or the equivalent will.

Have you tried involving her in helping with the baby, give her that special big sister role.

Doll role play give her real resources and demonstrate gentle touch and play.

I would in moments of calm use it as an opportunity to overpraise and have a group hug and announce it to dad how wonderful her behaviour was because ......and she gave baby big hugs.

It's a big thing having your parents to yourself then someone else takes over. As previously said set time aside for 1 on 1 time for your toddler.

There's loads of books that cover this subject for toddlers too.

I don't have two but my understanding is that punishment/time outs aren't particularly effective especially at this age. I've found the book "how to talk so little kids will listen" quite helpful with various ideas for redirection, communication etc. I listened to the audiobook as struggle to find time to read, their voices are annoying 😂 but I've used some of the ideas and they work really well.

Just please don't follow the above suggestion of doing the same thing back to her 😬

wow this is terrible advice! How can you tell a child that something is wrong if you then do it to them? Not to mention it’s literal child abuse!

Punishments and time out are pretty outdated methods now, sounds like she is struggling to adjust to baby. Carve out lots of one on one time with her when you can, demonstrate gentle hands and praise her lots when she is gentle and loving with baby. If she starts to hit or throw, remove her from the situation but sit with her and explain ‘I won’t allow you to hit/throw, I need to keep you both safe’ and wait with her, regulating until she calms down. It takes a lot of consistency but this approach does pay off (we had really similar behaviour with my 4 year old when he was 2.5). It’s a tricky age but will get better, there are some great books on authoritative parenting, Dr Becky’s ‘good inside’ is fantastic x

hitting a child is child abuse, no 2 ways about it. What age exactly is ‘of age’?

didn’t say to praise them for hitting? It’s about holding boundaries, removing them if they hit so they cannot continue, but remaining calm as you are the adult and the one in control of the situation. You cannot teach a child that hitting is wrong if you then hit them, that’s common sense. Fear based punishments just don’t work, all that happens is your child becomes scared of you and it totally breaks the trust in the relationship.

the part of your brain responsible for decision making and understanding consequences doesn’t mature until 25yo.. a 2yo doesn’t know right from wrong, that’s what you have to teach them.

Not going to go back and forth with you as we clearly have 2 very different parenting styles, hopefully by the time your child is 2 you’ve had a change of heart.