+1 w/ valve stem seal weep @ startup causing some exhaust smoke - get that here also: an oil/filter change and a bottle of fuel system cleaner in the tank helps keep it under control.
You state the vehicle runs & drives well, just the noise is a concern: and has been happening for awhile.
I think pulling the exhaust manifold heat shield and checking the exhaust manifold for integrity: the exhaust manifold gasket, and exhaust donut (manifold <-> front pipe) gaskets makes sense. (Especially if the flex pipe was R&R'd / replaced and the exhaust donut was not.)
A quick exhaust system check would be to have a helper place their (leather gloved) hand over the tailpipe at cold start: any exhaust leaks would be amplified, if present.
With an engine cold startup, you should be able to feel any exhaust pressure being "bled" without touching hot metal. Might take a few tries (shutting down engine, letting cool to cold, restarting) to fully check though. (* This is a check you will want to do quickly, before the exhaust starts to heat up to operating temp.)
re: 106k miles on TB and components - anything belt-driven (idler/tensioner bearings, water pump, edit: oil pump) under the timing covers, or externally (power steering pump, A/C compressor clutch, alternator) is going to sound "loud" in the engine compartment if it has any issue: and can be a daunting challenge for any DIY'er to diagnose: let alone line techs / mechanics in the field that see vehicles every day.
Can tell you from experience w/ the '00 Camry & other vehicles - that a tired / worn water pump may "make a racket" - that can mimick other engine noises.
A decent mechanic's stethoscope (OEM, Lisle) for 20-30 bucks may be a wise investment.
I've also used 24"-32" lengths of 1/2 - 3/4 inch ID heater hose, to help narrow down an area, or component.
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There may be (?) an issue internally w/ the motor, can't say / dunno / don't want to lead you "down a wrong path".
The above checks are low cost, DIY-capable, and things I would check, if here.
Hope the feedback helps.