Is there any way to measure electromagnetic radiation between 1khz and 30mhz?

If you do not mind a meter with a large antenna ( that does not fit in your pocket ), i would recommend in your case a Gigahertz HF, preferable one with sound ( like the HF35C or the HF38B ) which helps to identify the type of the predominant radiation.
You could also wait in the hope that the frequency range of the HF38B will be extended within one or two years to include the 5G band from 3 to 4 GHz.
https://www.gigahertz-solutions.de/en/measurement/high-frequency/hfrf-overview/
https://www.gigahertz-solutions.de/en/5g/frequencies-and-meters/
Never measure within a meter from an emf source like a modem or a mobile phone, as that may damage a meter.
More handy to carry around and cheaper are the Cornets, which seem to me a better deal than other low quality RF-meters.

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These are not "mine", i'm just responding and trying to help.
With a crab internal wide range antenna inside the Safe&Sound, what can one expect ?
Compare it for fun with :
https://www.aaronia.com/Datasheets/Antennas/Omni-directional-Antenna_OmniLOG30800.pdf
Of course some of the deviation may be corrected by the device in theory, but better do not count on that.
With an external and larger 600 euro wide range antenna, the frequency response curve is still far from good.

The Safe&Sound is new on the market, the Cornets have been improved during many years, and are much cheaper.
So if you want a crab meter, a Cornet likely gives better value for buck.
This is my estimation, do as you wish.
A RF-meter with a log-per antenna is bound to be clearly superior to one with a cheap internal antenna.
An exception, if any, would only prove the rule.

I do not remember to have written or read anything about 1kHz or 50kHz regarding the probes.
An ME3851A is supposed to handle this area and should work at normal distances.
and/ or consider something like this : https://aaronia-shop.com/products/mdf-magnetic-direction-finder
Well, that is also rather pricey unfortunatedly.

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i would rather see independant and proper testing than any supplied curve or specification.
in my view you simplify and ignore a lot, good luck with it anyway.

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Your approach sounds good.
However you do not get or forget half of what i wrote, and perhaps it is also a lot of nonsense, whatever, i won't keep answering.
The RF-function of the TF2 is rudimentary ( very crappy ) but this pleasant to work with instrument is much cheaper and includes reasonable electric and magnetic field meters, the latter even in 3D, although the weighted scales seem not that reliable.
As a layman i already noticed four tricks in the test by the makers of the Safe&Sound, so there are probably a dozen or so.
For instance it is the small peak-hold numbers on the TF2 that matter for these short pulses and these remain vague and ignored.
The intonation of the voices in these promotion videos also indicate dishonesty.

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The new Esmog Spion seems available for purchase.

https://www.priggen.com/5G-Esmog-Spion-Broadband-Receiver-50Hz-8GHz
or
https://www.endotronic-gmbh.de/messger%C3%A4te/5g-esmog-spion/

Here are some videos with the new Esmog Spion 5G:
https://vimeo.com/user127183542

black-sun wrote

I want to know whether there is a way to measure electromagnetic radiation between 1khz and 30mhz with reasonable accuracy without spending a fortune.

...

If that's not possible at a reasonable price, I want it to be at least 200khz.

Probably. For example this detector should work from 100 KHz to 500 Mhz, and detect signals as weak as -75 dBm with +/- 1 dBm accuracy:

https://www.ebay.com/itm/AD8307-0-1-600M-RF-Logarithmic-Detector-75-15-dbm-Measuring-Power-Meter/143683912576

(I think the 600 MHz upper limit is a typo, and the 100 KHz lower limit probably has to do with the design of the board.)

It's based on this chip, which is from a reputable manufacturer and is supposed to work at frequencies below 1 KHz:

https://www.analog.com/en/products/ad8307.html#product-overview

You would still need different antennae for different frequency ranges.

I just ordered a similar board based on the AD8318 chip from Analog Devices, which is supposed to work from 1 Mhz to 8 GHz:

https://www.ebay.com/itm/AD8318-RF-Logarithmic-Detector-RSSI-Measurement-Power-Meter-1-8000MHz-70dB/333845892085 (There are cheaper sellers.)

Another option would be a board like this, which should work from 100 KHz to 2.5 GHz and be sensitive down to about -60 dBm:

https://www.ebay.com/itm/1PC-AD8313-RF-Power-Moudle-Meter-Logarithmic-Detector-Power-Detection-Broad-bn1/124390398267

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