What are the dangers of operating a mini excavator?
OSHA has a search engine.  Many accidents are not reported to OSHA, in particular, amateur/homeowner operators like you don't have a reporting chain to OSHA.  But here are those OSHA knows about.
Obviously the vast majority involve the operator injuring others.  I omitted them since you say you'll be a lone worker (which has its own set of risks...)
The following contains descriptions of serious injury and death. Reader discretion is advised
Stuff they brought down on their own heads

At 11:00 a.m. on May 5, 2020, an employee was operating an excavator (KOMATSU Model PC240LC, mid-size hydraulic excavator) to jackhammer the base of a concrete silo so that two coworkers operating undescribed heavy machinery with one inch cables attached to the silo to pull it down once freed from its base. As the employee was jackhammering the base, the silo collapsed and fell onto the employee's excavator. The employee received unspecified fatal injuries from the falling silo material and was killed.


At 3:30 p.m. on August 2, 2019, Employee #1 was clearing trees and brush from a lot, using an excavator. One of the trees fell on the cab of the excavator and killed Employee #1.


At 4:00 p.m. on August 7, 2018, an employee was installing steel shoring in an excavation. The excavator inadvertently released the steel shoring plate which fell onto the employee. The employee was hospitalized with multiple rib fractures and a wrist facture.

Hit power lines

At 4:30 p.m. on April 13, 2020, Employee #1, employed by a pumping company, was working at a construction site. He was operating an excavator to drill a point well. The excavator became energized by an overhead power line. Employee #1 sustained an electric shock. He was transported to the hospital, where he died.

By the way, the machine chassis has a fair chance of protecting you while you remain in the cab, because the whole metal machine will tend to be one voltage (whatever it is touching).  There's no harm in being at one voltage, even if it is 21,000 volts.   The dumbest thing you can do is try to climb out of the machine at that point, because you'll be touching a) the energized machine and b) earth. Either stay put and call 911, or if able, move the machine to disengage from the wires.  But if the wire is downed, get hundreds of feet away from a downed wire before thinking of climbing down, as a voltage gradient can carry some distance.  And always report the strike to the power company; the strike may have broken insulators or weakened a wire that will drop later.
Lost stability due to terrain

At 3:15 p.m. on February 15, 2019, an employee was moving a Takeuchi Model TB007 Mini Excavator Serial # 1074544 down a ramp to the basement of a building to be stored. The equipment rolled over down the hill several times landing on the employee at the bottom of the ramp resulting in fatal injuries and bleeding. The equipment was not provided with roll over protection.

Self-inflicted tipping/rollover not caused by terrain
It's perfectly possible to rollover an excavator on flat ground without digging any holes.

At 11:00 a.m. on September 10, 2018, an employee was operating an excavator to move tree brush from the bottom of a hill to the top. While moving the load of brush up the hill, the employee moved the boom which cause the excavator to roll over onto its left side. The employee, who was seat belted into the cab of the excavator, hit his head on the roll over protection system frame as the roll over occurred. The employee was taken to a local hospital for treatment of a head laceration.

Pinned by ones own machine (not due to tipping/rollover)

At 3:30 p.m. on May 26, 2020, an employee was operating an excavator. At some point, the employee stuck their head out of the excavator cab while the cab rotated in close proximity to a tree. The employee's head was caught between the cab and the tree and crushed. The employee was killed by traumatic head injury.


At 11:15 a.m. on February 25, 2019, Employee #1 was operating a John Deere 225d excavator. The employee attempted to adjust the mirror on the excavator so that he could continue backing out of building to clear the doorway. He pulled the shut off lever and leaned out of the cab to fix the mirror. When he reengaged the safety shut off lever, he was inadvertently leaning against the joystick that rotates the cab. The employee was struck by and caught in between the excavator cab and the building's door opening. The employee used the joystick to rotate the cab back to the right, and freed himself. Employee #1 sustained three fractured vertebra and a broken collarbone. He was transported by ambulance to a nearby hospital and remained hospitalized for treatment.

Loading and unloading the excavator off the trailer
Needless to say, several accidents involved the operator trying to load or unload the excavator from the delivery trailer for highway transport.  Honestly, I forgot them because I was in the mentality of searching for accidents where the operator is in the cab.  But yeah, during load/unload, a lone worker can fall, get pinched e.g. have the unit shift on them, rollover while loading, or be tempted into &quot;hold my beer&quot; tricks of radical self-loading.

src
&quot;What could possibly go wrong?&quot;
(full disclosure, that last is actually a patented, engineered kit. The excavator has guide wings welded to frame and bucket. Once up top, it can move down the entire train of same-height cars, by expanding or contracting like a ... um... caterpillar.)