I'd like to burn thirty mp3 songs to a CD-R, using say cdrecord. But I'd like to
use my laptop for other things at the same time (such as using the Kate editor
and the Internet).

However, I've read that if the laser is writing to the CD, and the process is
interrupted, the writing is spoiled.

My Question:

So how can I make cdrecord and the CD recorder have uninterrupted use of system
resources, while still allowing me to do other things on the system?

linux itself is multitasking, so this cdrecord will never run alone. Actually you may try to run a terminal emulator, an editor or browser next to it just you must not overload your system. But better to be on the safe side and be patient.
You may also try to increase the priority of that process if you wish.

I think this problem occurred with very old cd writers, around 2000 or older. Related articles I found in the web are referring to ms windows nt4, 2000, xp. Drive's buffers were small at the time. The drive's internal buffer memory stores some data to burn, another buffer stores more data in the PC's ram and burning software manages so that these buffets are kept full as much as possible. If you don't do any other work on the pc, the buffer will be full from 97% to 100% and the burning process will be safely done. It you do disk intensive work there are chances that the data transfer can be slow or even stop for a few seconds. Another problem can be burning data from a network connection. Network speed is never guaranteed, so there is risk to be out of data in case of interrupted or slowed down connection (it's safer to copy files to burn on a local hard drive before burning). Screen savers and power management/sleep utilities have to be inactive for further safety.

I personally left always the computer alone during burning. This isn't really hard to do, as burning times are short at a burning speed of 16X or 20X (4-5 minutes max for a full cd). This wasn't always the case: I remember the first cd writer in my job's company, a Yamaha 2X in the late 1990s. In addition, the burning software supplied by the manufacturer didn't support correctly the specific model and burning could stop with no apparent cause.

Not running other software avoids problems from any eventual issue from other software like a web browser or a music/video player.

Nevertheless, since 15 years or so drives are able to stop momentarily burning according to the buffer's content, and restart burning after buffers get data again without damaging the cd burning, all this as part of the same recording session (nothing to do with multisession recording). This gives an extra safety, however I don't know how this is handled by the burning software.

I have frequently burned optical disks while doing other tasks on the computer (on multiple computers over the fast 17 or 18 years) and never encountered this issue in doing so.

I've encountered other issue (dodgy media, bad downloads, etc.), but not this one.