From a Professional Technician standpoint (Closed down my full time small engine shop & echo dealership in 2020) - Fuel issue- For one thing the addition of Ethanol alcohol to the fuel does accelerate the deterioration of all the rubber, and even some plastic parts - Fuel lines, diaphragms, filters, and more (Some Poulan/Craftsman were notorious for their fuel caps distorting due to the plastic material swelling - Always kept fuel caps in stock)
Diaphragms in the carburetor if they sit for too long can and do become stiff, and can take several (5-15 minutes) run time alternating between idle and full throttle to "loosen up" - Often however folks (or technicians) were too impatient and started fiddling with carburetor adjustments , then they would bring it in to the shop because it wouldn't run right and needed adjustment. (Many models of various brands can be rather sensitive to having carburetor adjustments done following a strict factory procedure, with accurate tachometer, so often they need to return to a shop equipped with the know-how and specialized tooling to do the adjustments)
As for a little more thought on the idea behind buying mid grade or premium gas - Bear in mind that engines are designed around a minimum octane rating fuel , typically 87 octane - 10% ethanol fuel (E-10) , if you remove the 8.7 points of octane (in theory) of the added Alcohol, you have a very poor quality fuel that is going to cause many problems (pre-ignition, detonation, overheating, hard starting, improper operation, and more) - How do you remove alcohol from fuel you may ask? Easy: Just add water. Ethanol fuel is hygroscopic, it will absorb moisture from the air (Hence desirable to keep gas in air tight containers, but even then, you can get condensation inside the gas can) Once it absorbs enough moisture, the weight of the water can cause it to drop out of suspension (Which is when you get visible water in fuel) well, that water is bonded with the ethanol alcohol , and thus separating the alcohol from the fuel.
So, Echo recommended 89 octane or better grade, on the theory that even if your alcohol separated from fuel, you would still be left with a fuel that had a high enough octane rating that wasn't gonna destroy your expensive chainsaw.
As a matter of shop POLICY in my shop, on 2-stroke engines that came in, (unless we had service history that would indicate otherwise) Fuel system components (Lines, Filters, Tank Vent, purge bulb, gas cap or gasket) would be replaced every couple of years, whether or not they were a source of a problem. It was just plain maintenance - Same with all the 4-stroke gas equipment - Fuel lines, filters, hose clamps grommets; from tank to carburetor were ALWAYS replaced every couple years (or if no service history with us, whenever they came through the shop) as much as 25% of the time, just that simple maintenance process solved the problem the machine was in for in the first place.
I never bothered with that over-priced fuel in a can stuff (Seriously, 12 bucks a gallon for gas???) However, I would often dump out an aged can of gas (If it had been more than 3 months since it was filled) into the truck's gas tank and get fresh fuel. Even modern ethanol-free fuel deteriorates far more quickly than gas used to - as little as 90 days before it starts to go bad and cause problems - So, policy was to track fill up dates on gas cans (I kept mine numbered and just wrote on calendar when they got refilled) and I recommended the same to customers.
Upshot of it was, my shop had a reputation - Might be more expensive than everybody else, but well worth it if you wanted something fixed right. All my regular loyal customers also often followed my advice as above and tended to have very few if any problems, and their equipment lasted a good long while. The downside to that was to myself- If you fix things a little too good, you don't have the customers coming back as often to sell billable hours to, and most of the folks that ran cheapo box-store stuff (Poulan, Craftsman, etc) found that it was cheaper for them to go buy a new chainsaw than to have me (or local shops) fix their old one , once labor rates started hitting the $40-$60/hour level in the '00s - Eventually it reached the point that with the pandemic putting a halt to many things, plus declining business (most of my best customers were wealthy retirees and they had a bad habit of dying off), skyrocketing shipping costs (I had a sizable Ebay presence, approaching half mil a year), and increasing government regulations (EPA, State DEP, Taxes, you name it), and I closed down.
So for the O.P. I might suggest starting with the simpler stuff: Make sure switch is on, pull spark plug and check if it is wet with fuel (if it is, turn saw upside down , switched off, and pull starter cord a number of times to help clean it of excess fuel, blow plug dry or put in a new plug, and re-test - If it keeps flooding, your carburetor diaphragm is probably stiffened and keeping the metering needle off the seat) , Fuel lines are a very common trouble spot so simply replacing all the fuel hoses (one at a time is recommended) may solve the issue, Fuel filters, even if they look clean, can still be plugged or restricted... Fuel tank vents that are clogged can allow fuel tank to over-pressurize and push fuel straight through the carburetor.... Or, if too much for you, you'd have to run it in to a shop, but bear in mind, it might be cheaper to just buy a new saw with warranty on it (I still highly recommend Echo, if you find a good Dealership, the factory does back up their 5 year warranty...to the point they will tell dealer to just give customer a brand new saw to replace a 4-year old machine that needed a fuel tank...)