Can you suffer from burnout after a loved one's death?

Absolutely someone could be suffering the effects of caregiver burnout after it has ended. You are also experiencing grief over the loss of your grandmother, and a new job on top of it. Your whole life has changed very fast. There was no transition period for you to just take a break. Even when there is it's still hard to get out of living in what I call "caregiver time". When someone is a caregiver to an elderly person every moment has to be carefully planned and on a strict schedule. A person needs some time to transition back to a normal life.
Give yourself a break. A few years ago my full time paid caregiving job ended abruptly. I worked for one invalid who was bedbound from LBD. Then my father died in the nursing home six weeks later. He was still new to the place so I had these people harassing me night and day. One time their business office has called 17 times in one day. It didn't even stop on weekends. Every waking moment of my life was about an elderly person, their care, and who's getting their money. Of course my own elderly mother was still sniping at me night and day.
Even though it all stopped, I was couldn't just snap out of crisis mode and living on caregiver time. Every time the phone rang I was overcome with dread. The nursing home wasn't calling anymore. I wasn't working for the invalid client whose family depended on me for everything anymore.
I had plenty of money and did not have to go back to work right away yet I was so exhausted I could barely get up from bed in the morning.
You need to take a break even if it's a little at a time. Make a date to go out with friends once a week. Do something you enjoy regularly. Like go to a movie or taking a daily walk. Go on vacation if you can. It will help.

My 100 yr old mother passed on January of this year. We collected her things from SKN and completed her funeral arrangements.

After eight years, I am trying to get in touch with what I need. What do I enjoy(?) What is my future plan(?) I looked up free online training courses in the programming language SQL and attempted the first lesson. After a total mind freeze I closed the session discouraged. Walked away. Twenty minutes later, something clicked and I went back into the session and completed it (!)

Spring is here. Pussy willow, crocus, snowdrops. Trees getting their buds. I remember something like “no Winter lasts forever, no Spring misses a turn”. Let it happen.

Yes, burnout lingers!! I was with Mom daily for 15 years, with the last 5 serving in a caregiver role. When she passed a couple of months ago at 100, I found myself feeling totally exhausted. I don't think years of this type of emotional and physically exhausting care can be remedied in a few months. Take all the time you need, go slow, and give yourself permission to rest.

You are still grieving your grandmother's death. If you were her caregiver, your grief reaction will be more intense. Depression, lack of patience, no motivation, inability to concentrate. --all entirely normal.
Try writing out some of your feelings. You can buy a notebook or composition book and write down what you are feeling, write letters "to your grandmother," write about your sadness, your anger your confusion--anything that comes to mind. No one else ever has to read these things. You can throw your notes away if you want to, but writing them down helps you recognize and articulate your feelings and puts your thoughts somewhere outside of your head and off "the hamster wheel" that is clouding your brain and your ability to function.
Getting back to what is more normal for you can take time. Don't rush yourself. It takes as long as it takes. There is no "should" in grieving.

A friend who cared for her FIL for years is just now bouncing back almost a year after his death. She and her husband have had to deal with the FIL’s house and finances since his passing, so the “job” continued for months. The return of her freedom to be herself is a bit overwhelming! It is what I crave and I warned my family that when the time comes and Grammy is no longer with us, I am going to disappear for a long while. No plans, but the sure knowledge that I will need time. Give yourself time and be gentle with yourself. Grief is definitely a process.

Give yourself a break.
There's no norm for this. Only you know how you feel, so allow yourself to grieve and mourn as much and for as long as you need. For many, it takes as long as a year to get back to some sort of normalcy.

My mother is still alive. But I experienced what you described once she moved into care. It’s as if I held it together for her, and the moment that constant responsibility was lifted I fell apart. Exhausted, unable to focus, waking at every little sound, anxious and jumpy, just staring out the window or at the tv. Months later I am still not quite myself.

Sounds like you are still fulfilling a lot of needs but your own. Give yourself permission and time to grieve, and to recover, physically and emotionally.

https://grief.com/the-five-stages-of-grief

Perhaps you can locate a grief counselor in your area. I found that by doing volunteer work, it got me out of my own depressing thoughts and gave me hope.

I came here to say what ConnieCaretaker has already said; you're likely suffering from the 5 stages of grief rather than 'burnout', and likely feeling Depression right now, more so than anything else.

The 5 stages, which fluctuate, are:

Denial
Anger
Bargaining
Depression
Acceptance

The sixth stage is thought to be Finding Meaning, b/c many caregivers lose themselves during the long, arduous road they found themselves on for so long. Then after the loved one dies, they ask NOW WHAT?

The link Connie provided you with goes into detail about the 6th stage and offers a book about the entire subject matter. Excellent site to check out.

Wishing you the best of luck with your situation.

Please consider a few things to try to help you:

1 - Go see a medical doctor. You may have some physical issues that need to be addressed so you can feel more energetic.

2 - Go see a psychiatrist of counsellor that can help evaluate and treat mental health issues. It is not unusual for death of a loved one to create all sorts of feelings. Dr. Kubler-Ross outlined the usual process of grief stages:
Stage 1 - "denial" - the feeling that this can't be true
Stage 2 - "anger" - the feeling that this isn't fair or right
Stage 3 - "bargaining" - ineffective methods to bring back the usual or normal life before the loss
Stage 4 - "depression" - the sadness when realize the loss is permanent
Stage 5 - "acceptance" - the feeling of peace and wholeness after the loss
You might just be going through the depression phase or you might have some underlying depression which can be treated successfully.

3 - Make time to recharge your "batteries" daily and weekly: sleep 7-9 hours every day, do something enjoyable to at least 1 hour daily and more so on days off, and develop friendships with people who nurture you.

4 - Consider nurturing your faith. As a Christian, I find that time spent talking to God and reading His words to me help me to feel more at peace and focused.