Some 2021 Census is now available on the ABS TableBuilder site, allowing additional analysis of the social and personal characteristics of higher education students. This posts looks at migration status and language spoken at home, previous strong predictors of higher education participation rates.
Year of arrival
In 2021 migrants who had taken out citizenship were significantly more likely than people born in Australia to be enrolled in university in the post-school 18 to 20 years old age bracket. The participation gap was 19 percentage points for migrants in the decade prior to the 2021 census, 54 per cent participation compared to 35 per cent for young adults who were born in Australia. Migrants who arrived as younger children have a higher participation rate again, at 59 per cent.

Language spoken at home
The 2021 Census finds that some language groups have very high participation rates. Young adults who speak Southern or Eastern Asian languages at home have participation rates that are more than double those of people who speak English at home. Possible reasons include high rates of family arrival through the skilled migration program, creating the usual association between the education of parents and children, and cultural attitudes favouring higher education. (A majority of 18-20 year olds in most language groups were born in Australia.)
For young adults speaking Arabic or African languages at home, with family arrivals in Australia less dominated by the skilled migration program, participation rates are also well above English speakers or the general Australia-born population. People speaking Pacific Island languages, however, are less likely to go to university than the other groups. Disaggregating some of the larger groups a couple of small language groups have lower participation rates than English speakers, Maltese (31 per cent) and Hmong-Mien (30 per cent). Each have fewer than 200 people in this age group speaking the language at home.

One change between Census 2016 and Census 2021 was that 18 to 20 year olds speaking Southern Asian languages overtook their East Asian language speaking contemporaries to become the most higher education focused language group. They moved from slightly behind to slightly ahead, but the change is still interesting given that Chinese-background families are often thought of as standing out for their extreme emphasis on higher education.
The chart below shows Southern and Eastern Asian language groups with over 1,000 home speakers in the 18 to 20 age group with the highest participation rates. My ability to match geographic locations with Southern Asian languages is not going to win me any quiz show prizes, so I added Wikipedia based information on where they are typically spoken.

Other Asian language groups – Indonesian at 69 per cent, Vietnamese at 66 per cent, Japanese at 62 per cent, Filipino at 58 per cent and Tagalog at 57 per cent – also have high rates of university attendance.
An important contextual point is that most citizens (84 per cent) and citizen higher education students (75 per cent) in the 18 to 20 age group speak English at home.
A caveat – citizens versus permanent residents
The Census is weak on identifying residency categories. I put an Australian citizen filter on to avoid counting international students. However this means I excluded permanent residents. The distinction is important for my analysis because permanent residents are entitled to a Commonwealth supported place but not in most cases for a HELP loan. This creates a financial incentive to become a citizen, as HELP is the only government benefit I have found that is available to citizens but not permanent residents (in 2017 I argued that this distinction should be dropped).
For migrants from some countries of interest, however, permanent residents not planning on higher education have an incentive not to take out Australian citizenship, because their home countries do not allow dual citizenship. This includes China, Hong Kong, Singapore, Malaysia and India. Their citizens are a potentially biased group for higher education participation rate analysis, of people who took out citizenship to get a HELP loan.
For the 2016 Census the ABS used linked immigration data to produce a separate dataset for permanent residents. As expected, permanent residents have lower higher education participation rates than citizens, but combining the two groups only takes six percentage points off the Southern and Eastern Asian language group participation rates, leaving their overall 2016 participation rates at very high levels. Upfront student contributions do not stop the PR-only young people from these language groups exceeding the participation rate of people who speak English at home.

Further research
The current release of the Census TableBuilder supports further analysis that could be interesting – putting on a completed Year 12 filter (although this is a weaker proxy for being on a higher education track than it was in earlier decades), looking at ancestry and parent country of birth, adding in attending vocational education, and gender.
Non-English speaking background arrivals on the last decade are still an equity group, so further analysis is needed for that ten year arrival period. However on the numbers above it seems unlikely that equity group status can be justified. Removing the citizen filter and looking at language groups that are strongly represented in humanitarian arrivals might, however, identify sub-groups with different patterns of participation. Permanent humanitarian visa holders are an exception to the general rule that only citizens can access HELP.