Okay I will be honest. A true service dog is evaluated by a professional chosen by their temperament for the task and professionally trained. True, some breeds generally have a talent for certain services because they have been bred for thousands of years to a task (job) that can follow along the lines of a service need. BUT, even then they are weeded out depending on their temperament.
I have had GSDs (6..2 at a time) most of my life, one Rottie and am on my 2nd Doberman. I want a Corgi!

Not an expert but, I will say that if you are looking for help with:
"Example tasks include: fetching my phone if I'm in a situation where I can't get it, assisting if I'm having a anxiety/panic attack, MAYBE training to use deep pressure to ground me, but definitely staying close by my side,etc."
GENERALLY I would say a Doberman be happy to fetch your phone, but would not be a good dog for the service of grounding you and helping with a panic attack. They are bred as working guard dogs and if you are having a panic attack they will turn full on protective and GUARD you from anything and anyone. This includes medical personnel, the police and your mom!
YOU will have to reassure the dog that you are OK. This could unsafe for the dog, support people and you.
The biggest difference I notice between GSDs and Dobermans is discernment. The GSD is in the herding group and the Doberman is in the working group for a reason. The GSD (herders) has been bred to problem solve and has an off switch GENERALLY. They will protect you, but if you need help and will let KNOWN other humans approach GENERALLY.
The Doberman (workers) has been bred to do a job, and that is to be your personal bodyguard. This means it wants to be with you 24/7 and is always looking out for threats (even if you don't see the threat ;-)) and will give their life to protect you.
They don't need to problem solve. If you are anxious and panicking they will read that as you feeling threatened.
Their first instinct will be to PROTECT you, not reassure you GENERALLY.
I say all this as a GENERAL assessment. You cannot pick a puppy out and know they will have the temperament for the service you require.
What I am trying to say is, (and this is just an opinion) find a dog that has been professionally evaluated for what you need. Tell them your breed preferences and they should be able to find an animal that will be a good fit. You will both be happier and safer.
I would like to add that I am using GSD as and example because I know that breed best.
I am very happy with my Joe and he is a very smart, fast learner. I can actually see him deciding he may want to please me sometimes. So funny!
He is starting to see some gray in his black and white world and to control his reactiviness. He does not need protection training unless it is to learn to be called off.
He is going to be an awesome dog. Maybe we can try SAR down the road since he is so nosy.