Is it possible for fat to enter the bloodstream (causing embolism) because of tumescent tickle liposuction?

yes there is risk of PE and DVT/embolism with fat grafting and any liposuction procedures.  Talk to your physician and get an expert.
You need a formal evaluation by an expert in body shaping and contouring to determine what is best.  Traditional liposuction awake and smart liposuction are old methods and do very poorly for tightening skin or significant skin tightening or contouring.  Small problem areas can be improved slightly by these methods.  The best in body contouring not only removes fat with energy devices like VASER ultrasound but also internally heat the skin with radio-frequency devices such as J PLASMA/RENUVION, InMode BodyTite, ThermiRF to heat the under surface of the skin and tighten it at the same time as fat removal. These combinations are called 4D HIDEF VASER contouring and can only be done by a well . trained body contouring specialist. At the same time fat should be harvested, PRP and stem cells added and injected into muscles or indentations/cellulite to get body shaping and contouring.  This is known as a Brazilian butt lift when you inject the fat to the buttock for contouring and lifting, but fat can also be used in areas such as the chest/breast, arms/shoulders, calves and face.  Cellulite should also be treated with cellfina, sculptra, subcision and/or fillers such as bellafill, renuva synthetic fat, or sculptra.  If skin is very loose before surgery then it will need to be removed such as lower abdominal skin (tummy tuck/abdominoplasty), breast skin (breast lift), arm skin (brachioplasty).  Overall you need a full assessment, but simple liposuction alone will not tighten skin and needs a combination of various methods -- fat removal, skin tightening, defining, fat grafting, skin removal -- to get the best in body contouring and body sculpting.  Dr. Emer.

Liposuction carries a very low risk of emboli since fluid is first put in to constrict blood vessels, and suction is applied with removal. During the BBL, if the fat was injected too deeply, there is a significant risk of emboli. With just liposuction, no fat is injected back into your body.

I understand your fear of fat embolism after the reports of them occurring in BBL.  however the risks from liposuction are quite remote especially by comparison to fat injection. The cause of fat embolism from fat injection is well recognized and liposuction has an entirely different mechanism of how it works.