TLDR: Crews for 1 bar missions, including Soyuz, don't seem to have ever used pre-breathing. Earlier missions that were headed for long-term lower pressure environments did, as do people doing lower-pressure space walks. There's some evidence that the risk of high-oxygen pre-breathing was considered larger than the risk of decompression sickness.
There's a NASA Human Research Program report on "Risk of Decompression Sickness" (link is to a non-paywalled undated version) that also discusses pre-breathe protocols. Astronauts for SpaceLab, Apollo and earlier were headed for flight environments at lower than 1 bar pressure and used pre-breathing. The Space Shuttle program, which had a 1-atm environment, did not have a protocol to pre-breathe before flight, but did use it for EVA.
The various descriptions of Soyuz crew timelines (here, here, here) don't seem to have any time for pre-breathing; suits are closed up only at the last minute, and crew photos show them walking and sitting without breathing masks.
What are the trade-offs involved in pre-breathing vs not?
An in-suit pressure of 0.4 bar is about 24,000 feet altitude equivalent; 0.27 is about 32,000 feet equivalent.
There's a 1999 NASA study "An Evidenced-Based Approach
for Estimating Decompression Sickness Risk in Aircraft Operations" that provides upper limits on the risk:
(The yellow and blue lines were added at 32k and 24k feet respectively)
These are for "healthy flight crews", not necessarily astronaut-level medical review, but the 0.27 bar line does show a significant chance of decompression sickness at longer exposures. Those probabilities have to be combined with the probability of a decompression event (a certainty for an EVA, but hopefully much less for a rocket launch) and the medical severity of the subsequent decompression sickness.
As an aside, their methodology provides some insight on that:
The typical flight profile for the NASA T-38 is an ascent to approximately 41,000 feet above mean sea level over a period of 15 minutes, cruise flight at altitude for approximately 1.3 hours, and 10 minutes for descent and landing. The cabin pressurization schedule is ambient pressure until one ascends to 8,000 feet (10.9 psi), maintains the pressure at 8,000 feet equivalent until one ascends to approximately 23,000 feet (5.9 psi), and above that maintains the cabin pressure at a 5-psi differential. NASA flight crew do not routinely prebreathe 100% oxygen and typically fly with the oxygen regulator (CRU-73/A) in the “normal,” diluter demand mode. The percent oxygen in the breathing mixture is variable, based upon the normal variability of the oxygen regulator, but is designed to maintain a sea level equivalent oxygen tension in the aviator’s blood.
Approximately 600 flights per year are conducted in NASA T-38's. A review of 20 years of aircraft operations safety data reveals approximately one cabin pressure system failure every two years, and no reported occurrences of DCS (Personal communication, NASA/JSC Safety Office, Ellington Field). Assuming 20 years of 600 flights per year and no observed DCS, the probability of DCS is no greater than 0.025% for each flight (95% upper confidence limit as
n 1/n expressed by solving (1-p) = 0.05 or p = 1-(0.05) ). An analogous review of USAF T-38 flight operations revealed 294 cases of cabin pressurization system failure for the years 1987 to 1992, at altitudes ranging from 17,000 to 43,000 feet (Personal communication, Headquarters, Air Force Safety Center, Kirtland AFB).
The decompression risk has to be weighed against the risks of pre-breathing pure oxygen. Oxygen with a partial pressure of over 0.4 atm (0.3 in some literature) is considered a medical hazard over multi-hour timescales. For example:
Prolonged exposure to above-normal oxygen partial pressures, or shorter exposures to very high partial pressures, can cause oxidative damage to cell membranes leading to the collapse of the alveoli in the lungs, retinal detachment and retrolental fibroplasia in the eye, and seizures. A decline in pulmonary function testing can occur within 24 hours of continuous exposure to 100% oxygen. After 48 hours on 100% oxygen diffuse alveolar damage, atelectasis, and acute respiratory distress syndrome (pulmonary edema) can occur.
(from J.S. Cooper et al) Other more recent work shows the possibility of onset at shorter times:
In healthy humans breathing more than 95% oxygen at normal atmospheric pressure (0.1 MPa), tracheobronchitis develops after a latent period of 4 to 22 hours
Four hours is only marginally longer than usual pre-breathing schedules:
A minimum 3-hr in-suit PB was performed before launch in all NASA programs prior to the Shuttle (Maio et al. 1970) symptoms consistent with DCS while at 5.0 psia. Michael Collins, during Gemini X and later during Apollo 11, believed he had symptoms of pain-only DCS in his left knee that eventually resolved in the 100% O2 atmosphere as the missions proceeded (Hawkins & Zieglschmid 1975). This was not an unexpected outcome based on previous PB validation trials reported by Maio et al. (1969, 1970). Astronauts on subsequent EVAs from the Apollo spacecraft and Skylab, as well as on moon walks from the Lunar Module, in suits pressurized to 3.7 psia were not at risk for DCS due to denitrogenation during their extended time in the hypobaric and hyperoxic breathing environment.
As an aside, there are other possibilities besides high-O2/low-N2 pre-breathe gas: Mixtures with either helium or argon avoid N2. But both of those gases add other complications: High helium atmospheres tend to diffuse into systems and packaging, and argon has physiological issues that require a lot of supervision during breathing. I didn't find any evidence that either was ever being developed for use in space-flight pre-breathing.