This is probably the most interesting question I've ever been asked regarding the Olympiad so far.
In terms of the patterns, I would say there are a few patterns regarding which topics come up and what they tend to ask. Sometimes they'll throw in a question that is themed about something that happened in the last year (though this usually doesn't require extensive knowledge of the event in question - for example, the Liz Truss cheese question that came up in 2023 just required you to apply knowledge from a range of A level topics to solve a couple of problems loosely connected to cheese rather than anything about her or recall anything niche about any kind of cheese lol). Expect moles, NMR, organic synthesis and unit cells to come up as they always do. NMR is usually limited to how many signals/peaks a given spectrum has (either 1H or 13C), organic synthesis usually is like filling in a crossword (you get a few hints such as the formula, spectral data and reagents used for an interconversion that may or may not be familiar). Unit cells you won't have done at A level and often require you to recall geometry from GCSE/A level maths - you will also have to learn a dedicated method for determining the numbers of atoms in a unit cell given the diagram (this I can talk you through if you want as it comes up every year).
Structure-wise, it is quite common for the individual parts of the same question often follow on from one another, which can be a pain if you struggle with the calculations and for each question to open with more straightforward parts and get progressively more challenging. Generally if you need an answer to an earlier part to answer a later part, they'll tell you to use a particular value if you couldn't get said answer. In terms of words to look out for, it's mostly the command words used you need to identify so that you don't lose sight of what the question wants you to do. These are generally limited to "tick", "give", "write an equation", "draw", "deduce", "calculate" and "determine". These are pretty much all used in A level exam questions and the meanings are all identical to what they are taken to mean in A level papers (imo these are all very self-explanatory, but the precise meanings of any terms that are not well understood can always be looked up in an index of command words, e.g:
https://www.oxfordaqa.com/oaqaresources/science/assessment/9620-international--as-and-a-level-chemistry-command-words.pdf).
In terms of what they test for, it's predominantly application of knowledge, but there definitely are questions that require you to have memorised little details in the specification and definitions (e.g the multiple choice questions). They tend to throw problems that are towards the A/A* end of A level at you in terms of difficulty, but they throw in stuff you won't have studied at all (i.e simpler topics from the first two years of undergraduate level chemistry) that you can work out with A level knowledge. In terms of niche things, it's quite unlikely they will come up - there are some small points on each A level syllabus, but it's highly unlikely you will need to recall these sorts of things in your answers unless they can be deduced from information they have given you. They have thrown unfamiliar reactions in the organic synthesis before, but often these are just unusual cases of reaction types you are familiar with (e.g if you see a carbonyl compound reacting with an organometallic reagent like CH3MgBr, it's nucleophilic addition with "CH3^-" acting as the nucleophile"). These are perhaps the closest types of questions to them assessing niche topics that come up frequently, I suppose.
Although you didn't specifically ask for this, I have some small recommendations for the exam and how to prepare. First and foremost, highlight words in the question. The command words and what you are required to draw, calculate etc are well worth making more easily identifiable as the questions can be quite wordy. Secondly, if you get bogged down on a part of a question, move on. It's better to do something with the time you are allowed other than stare at the paper without accomplishing anything - the starting parts of the next question (if there is one) are probably easier than the later parts of the question you are on. If you are considering a chemistry degree after you finish your A levels/equivalent, it may be worth getting hold of a copy of "Chemistry^3: Introducing inorganic, organic and physical chemistry" by Burrows et al as it is a very well-written guide to much of what you can expect to be assessed on in the Olympiad. You could also try seeing if a local library has a copy. With past papers, don't bother with anything pre-2017. A lot of these papers require you to have learnt stuff that has since been removed from the A level syllabus and worse still, some papers (particularly the oldest ones) are nowhere near the difficulty level of the more recent papers.