Why does it take so long to encode and authoring when I burn a DVD [video clips?

Time to process is related to software used and hardware used. Data starts on your hard drive storage. Spinning drives slower than SSD, and among SSD is faster and slower I/O. It processes through available RAM. Some of the system ram stores running processes, some is reserved for graphics storage in integrated graphics laptops and some is available to hold data fed into the CPU. The CPU processing speed is a factor in clipping, and any if any graphics changes are made, the graphics processor is a big factor. Everything in the hardware is a factor and is not listed in the question at all. The software itself does have a performance factor also.

Burn time to DVD is a data burn rate and the blank disc and burn  settings affect it after the pre-processing.

cpu benchmark is here:

https://www.cpubenchmark.net/cpu_list.php

But, you need to state what hardware you are running to know whether it is running as expected.

My laptop I just bought for about US$500 delivered has a 256gb ssd, 8gb ddr4 ram, Ryzen 5 3500U CPU score 7182. and integrated Radeon RX Vega 8 graphics at rank #310

https://www.notebookcheck.net/Mobile-Graphics-Card...

You may need to adjust to include archived graphics.

My old laptop A8-6410 cpu scored 1765 1tb slow spinning hdd, 4gb ram R5 Beema was rank 627 as much worse.

My new laptop is 4 times the CPU speed, 3 times the ram capability, and at least 5 times the storage I/O. My old laptop was slow at many things, and new one is much faster and is not an expensive PC in price range.

The video has to be decompressed a frame at a time, the recompressed to MP2 format before having the audio added back to create the DVD "VOB" format video files.

How long it takes depends on the CPU speed of the machine and if the program in use can use the GPU for any hardware acceleration (if it is capable of that).

And, it depends on the video resolution - how much data needs processing in each frame.

Each individual "Full HD" 1920 x 1080 frame expands to over six megabytes of data when uncompressed; 4K several times more.

Each DVD format video frame is around 1MB before compression.

What format are you using when you get the files from youtube?

DVD is not an HD format - for US NTSC they use 480 line video & for UK PAL, 525 lines.

If you are downloading videos in anything higher than 480 line format, all you are doing is adding extra processing time for each frame to be reduced to 480 line, with most of the detail content redundant.

720 line is way beyond any DVD version, but could just give fractionally better results for UK / European formats; whether it's worth the extra time is debatable.

1080 or higher is gross overkill and doing nothing but wasting time.