A couple of things:
All HP/Agilent/Keysight LCR/Impedance analyzers are made at the same factory in Kobe, Japan at "Kobe Instrument Division". Basically any model starting with 42xx or 43xx is a KID product, specifically so-called "Product Line 36" or PL36, and is some type of impedance measurement device. HP ran out of 4 and 5 digit numbers in the late 1990s so now it's E49xx for LCR meters now. So because this is a
4263A, it's KID and its an LCR meter. (Yes, pretty much ALL HP/Ag/Ks instrument can be broken down by their part numbers)
Both KID and HP/Ag/Ks' other Japanese division, HSTD (Hachioji System Test Division) were originally part of a joint venture between HP and Yokogawa formed in the 1960s, which was called "YHP" or Yokogawa-Hewlett-Packard. This joint venture was 100% bought out by HP in the mid-1980s. Occasionally you see old YHP logos but it's been absolutely disconnected from Yokogawa for decades. Yokogawa still has its own instrument product lines but there is no longer any interaction between them and HP/Ag/Ks.
HP got into this market because of the growing Japanese electronics industry in the 1960s but because they were not Japanese they were not accepted. Japanese companies buy from Japanese companies first and tenth. So HP got a Japanese partner, Yokogawa to build Japanese legitimacy in the local Japanese market - it took 20 years to stand on their own with the help of Yokogawa.
The reason for the linear supply is for the instrument side - you need low noise for most instrumentation so linear is the way to go. Switcher noise is problematic. The switcher is for the digital which is more forgiving and isolated from the sensitive analog front-end.
The handler interface is specially for testing surface mount devices (capacitors and inductors) using package part handlers which feed raw SMDs in and output tapes of parts that have passed spec and binned by performance - the LCR meter can automatically trigger binning by things like Q, ESR or value. So those reels of parts you use likely were tested with a KID LCR meter.
All the derived units like capacitance, inductance and other values like ESR, Q, etc. are "dumb algebraic derived" and depend on getting the perfectly corrected raw magnitude-phase value first which is where the Open-Short-Load come in - these are for correcting the fixturing that holds your DUT and getting that to "zero". The delta Ref is only for "icing on the cake" final correction where you have only one type of uncorrected offset i.e. only capacitance or only inductance or only resistance but never combinations of these - for these you need to use Open-Short correction because removing it requires a 2-port (4 distinct complex values) rather than a 1-port correction (1 distinct complex value).
The UI on all Japanese HP/Ag/Ks instruments suck - it's just how it is. Software is NOT their thing - building hardware is. The best UIs come from either Keysight Colorado Springs (where the scopes come from and which are the very best) or from Sonoma county (where spectrum analyzers and network analyzers come from). These are also the biggest and most profitable divisions so they can afford to invest in UI (which is not cheap). HP/Ag/Ks have always pushed profit-and-loss responsibility down to divisions/PLs and they also decide what to invest in for their product designs as part of this, so you see a far amount of variability across the entire corporation; but you avoid bureaucracy because decision are taken locally in a small group of people who know the product, technology and market best.
These are still great LCR meters because of both the accuracy and the measurement ranging, which far exceeds most lower cost units. The main reason is the methodology of measurement which is a "auto-balancing bridge" method. Most low-end LCR meters use a a RC/RL time constant method which is not amenable to manufacturing test but is good enough for incidental hobby and technician use. One thing you can only do with an bridge method is apply variable AC and DC bias while measuring the impedance which is important for ceramic capacitors and ferrite core inductors as these vary. Also you can measure far lower and high values better (most PL36 LCR meters can measure down into the fF range and up to F ranges). This makes even older units golden. I still see production test lines using 4284A and 4263A LCR meters even thought these have been obsoleted 2 decades (most recently a few months back).
I used to be the field applications engineer for PL36 (as well as others including PL1H which are products from HSTD and others). If you have questions on these, especially measurement theory about LCR meters or any other instruments generally, feel free to ask. I was trained on every instrument in the old HP catalog.
Also a good reference for LCR meters and impedance measurement is the Impedance Measurement Handbook which is written by KID.
http://cp.literature.agilent.com/litweb/pdf/5950-3000.pdf
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