Engagement is later than i like but I've found that to be true for literally everything manual I've owned.
Engine stayed running, but there was no power to the wheel. Also when I start it, there are no abnormal sounds until I pull the clutch in or shift into first.
Late clutch engagement that can't be improved by adjustment could mean the clutch disc is worn out. These discs are usually durable, functioning for 80K-100K miles or more depending on the riding styles of the users.
Difficulty downshifting can indicate lack of spline lube. Chronic lack of transmission input shaft spline lube contributes to wear of the clutch hub splines and/or transmission input shaft splines. When the teeth of a driveline splined shaft or socket are completely worn, power to the rear drive stops and is often accompanied by a grinding noise when in gear.
A YouTube video of the noise as shifting is accomplished while the moto is on the center stand might help us identify it. At the minimum, disassembly to inspect the rear drive and driveshaft splines, followed by removal of the transmission to inspect the clutch disc thickness, clutch hub splines and transmission input shaft splines is what I would undertake, based on your description.
Does the noise sound like this and are the circumstances that produce the noise the same?