I know this isn’t what you hope to hear, but the driver of a car has some reasonable responsibility to check the oil level via the dipstick on a routine basis. It’s what s called in the law “due diligence”.
If the oil had run out 10 miles after the oil change due to a loose plug then it would not be reasonable to expect a check of the dipstick to have prevented the damage, but if I understand your post correctly that’s not what happened. And IMHO you’ve gone too long without checking your oil to hold the shop that did the last oil change responsible.
You may also want to read the description in the owner’s manual of what the “oil life” montoring system really does. It does not monitor oil level. Even as regards to oil life, it assumes that the level is being checked. 1 quart of oil has probably 25% of the life expectancy of 4 quarts of oil. There’s simply less fluid to suspend contaminants, absorb the impact of dilutants from combustion blowby, and even absorb heat from the cylinder walls (which means the oil gets hotter). It relys on you to monitor the oil level.
The “genie lamp” if it were to come on would mean that the oil level had dropped to such a low leval that the top of the pool had gone below the oil pump pickup tube and you’d lost pressure completely. It simply says “serious loss of oil pressure - stop the engine NOW”. It too does not indicate a need to add oil, just a warning for not having done so until too late.
Honda has no responsibility in this whatsoever. An argument could be made that the last oil change place bears some responsibility, but the bulk of the responsibility IMHO lies with you for neglecting basic driver responsibility. I’m certain that your owner’s manual, dhould you read it, will recommend routinely checking the oil level with the dipstick as a driver responsibility.
Damage can occur without obvious metal shavings and a burnt smell. One of the main things the oil does is maintain a pressurized fluid barrier that holds sleeve bearings and their corresponding wear surfaces apart. Key ones are along the crankshaft and the camshafts. These surfaces if deprived of oil can seize together without creating loose shavings in a process called “galling”, where they basically transfer metal, essentially in a sort of welding process.
My hope is that you learn from this. Consider it an expensive class in basic maintenance.
I know this answer will not make you happy. It may even offend and anger you. I apologize for that. But this is the reality. People are trying to be kind about it, but in all honesty the biggest cause of the failed engine is neglect.
Sorry. That’s my honest opinion.