Will Canon's EF and EF-S lenses work better for Canon's mirrorless cameras than mirrorless cameras from other brands?

Canon has an official adapter for using EF and EF-S on their mirrorless cameras, but I have read that the focusing is slower when using this adapter than the native (EF-M) lenses.

Assuming the respective bodies are from the same marketing tier and have similar resolution sensors, you'll never get worse performance, either optically or in terms of AF speed/accuracy, out of an EF-S or EF lens when used with a Canon EF to EF-M adapter on an EOS M body (all of them use APS-C size sensors) than when using that same lens on a comparable Rebel or x0D body.

Again, EF-S and EF lenses will perform just as well on an EF-M or RF mount Canon body as they perform on APS-C and FF bodies, respectively, in the EF mount system when the cameras being compared have the same level of sensor technology and AF technology.

I have read that the focusing is slower when using this adapter than the native (EF-M) lenses.

Unlike when using an EF/EF-S lens on a non-Canon mirrorless camera, no EF autofocus or any other lens to camera communication has to be "translated" by the adapter when adapting any EF/EF-S lens to any EOS M or EOS R camera. The only reasons an adapter is needed at all is to account for the differing registration distances and shapes of the mounting bayonets between EF/EF-S, EF-M, and RF lenses.

Where you lose out when using EF and EF-S glass with EOS M and R Series cameras is when comparing them to the newer EF-M and RF mount lenses. The best RF mount lenses tend to be sharper and faster focusing than the best EF mount lenses with the same focal lengths and maximum apertures. They also tend to be modestly to exceedingly more expensive. As the saying goes, you usually get what you pay for.

Remember, there are more expensive and/or newer EF mount lenses that focus faster on the same EF mount bodies than cheaper and/or older EF mount lenses focus on those same EF mount bodies. Many EF/EF-S mount lenses also focus faster on higher tier and/or newer EF mount bodies than those same lenses focus when used with cheaper/older EF mount bodies, too.

The EF-M autofocus protocol is exactly the same as the latest revisions of the EF/EF-S AF protocol. If EF-M lenses focus faster on the same EOS M body than an adapted EF/EF-S lens, it's because the EF-M lens has a faster AF motor than the EF/EF-S lens, just as there are some EF/EF-S lenses that focus faster on the same EOS bodies than other EF/EF-S lenses can focus on that same EOS body.

Incidentally, due to the very small 2mm difference in the registration distances of the EF-M an RF mounts, as well as the differences in throat diameter and the shape and depth of the bayonet lugs (which exceeds 2mm), it's physically impossible to adapt an RF lens to an EF-M camera and have focus at any distance beyond macro distances without using additional optical elements that also act as a teleconverter.

The Canon RF autofocus protocol is an enhanced extension of the EF protocol that is fully backwards compatible with the EF AF protocol. EF and EF-S lenses will perform no worse on an EOS M camera or RF mount camera than they are capable of performing on an equivalent EF body. In some cases, second generation RF mount cameras like the R5 and R6 can focus the same EF/EF-S lens noticeably faster than the lower tiered EF mount Rebel series and older models of the x0D series of cameras can focus those same EF/EF-S lens. (Newer EF mount cameras, such as the EOS 90D, can sometimes AF faster with certain EF/EF-S lenses than an older or lower tier EOS M body can AF with the same lenses, though.)

Sure, EF-M cameras will almost certainly focus slower than Canon 1-Series cameras that use the EF mount when using the same lens, but entry level Rebel cameras that use the EF mount also focus the same lenses slower than their 1-Series counterparts, even though they are both EF mount camera bodies.

If you use an EF-S lens with a full frame EOS R body, the image will be automatically cropped to use only the center of the FF camera's sensor that is the same size as APS-C sensors. So that 20MP FF EOS RP becomes an 8MP APS-C camera when adapting an EF-S lens to it. The 45MP EOS R5 becomes a 17MP APS-C camera when an EF-S lens is adapted to it. This is necessary because the usable image circles of EF-S lenses are only large enough to cover that smaller APS-C sized area.

I want the camera to be easier to carry around for long sightseeing/tourism trips, but still be customizable with lenses.

With regard to smaller and lighter, though, there's not really much of a loss of total size/weight when going from the best EF lenses on EOS EF mount bodies to the best RF lenses on EOS R bodies. Much of what you lose with the body is often gained with the lens. There's also less difference in size/weight when going from the smaller, lighter lenses with narrower maximum apertures in the EF-S system to the lenses in the EF-M system than there is when going from larger and heavier higher performing EF lenses to smaller and lighter EF-M lenses with narrower maximum apertures. There's even less difference when using the same EF/EF-S lenses with an EOS M body plus adapter than when using the same EF/EF-S lenses with one of the smaller and lighter EF mount bodies.

This is also the case with most other manufacturers of mirrorless systems. Have you seen the size of some of the Sony GM E-mount lenses? Or the Sigma ART lenses for mirrorless mounts? They're about as small and light as a full mayonnaise jar. Sure, most EOS M bodies are smaller and lighter than most EF bodies. The EF mount Rebel SL series might be slightly smaller than the largest EOS M cameras, though. The Rebel SL series is certainly smaller than the larger models in the EOS R series.

In the specific case of your 60D, the only EOS M camera that has comparable performance in terms of things such as Servo AF, frames per second, etc. is the EOS M6 Mark II, which also happens to be one of the larger/heavier EOS M bodies, especially if one adds the optional EVF to the M6 Mark II hot shoe. (Of course tying up the hot shoe as the only way to have an eye level viewfinder, coupled with the lack of a PC port¹ is the M6 Mark II's Achilles heel, in my opinion, as it means one can not use an eye level viewfinder and control external flash at the same time!)

To get an RF lens that performs as well as, say the EF 24-70mm f/2.8 L II, one must use the RF 24-70mm f/2.8 L IS, which is just as large and heavy as the comparable EF lens.

_{¹ PC in the context of flash photography has nothing to do with a personal computer. It is an abbreviation of Prontor/Compur. Prontor has its origins in the Italian word pronto (quick) and was a brand of shutter produced by Alfred Gauthier in the 1950s. Compur, derived from the word compound, was the shutter brand of the Deckel Company. Both companies were based in Germany and both counted Zeiss as an influential stockholder when they introduced the standard 1/8"-inch coaxial connector for shutter/flash synchronization.}