How do the properties of different polysaccharides relate to physiology? (How will I be using/what should I be aware of in regards to polysaccharides moving forward in physiology?)
I would say that some of the most common polysaccharides in the context human physiology that you should be aware of are glycogen, glycosaminoglycans, and glycoproteins.
Glycogen is a series of glucose monosaccharides in a chain with alpha C1-C4 links and branches with alpha C1-C6 links. This molecule is highly branched, which allows it to serve as a very dense source of energy storage in the human liver.
Glycosaminoglycans are linear repeating disacchirdes(ABABABA....), of which there are many examples. They are frequently negatively charged at pH 7 and can play a variety of roles in many parts of the body: hyaluronic acid is a joint lubricant, chondroitin sulfate is a component of cartilage, and dermatan sulfate is found in the skin.
Last glycoproteins are proteins that have a oligosaccharide component. The "post-translational modifications" to proteins are extremely common throughout biochemistry, so it is important to be aware of. These oligosaccharides may serve as a marker for cell recognition (as with bloodtypes!), ensuring correct protein localization, or to alter/ aid in protein folding during synthesis.
(if you are interested in plant physiology consider also cellulose and amylose/ amylopectin since these are for involved in plants' structure and energy storage, respectively)
Moving forward in physiology, you will likely not need to know the structures of specific oligosaccharides, but you will benefit from recognizing when a polysaccharide is responsible for a physiological event- such as glucose storage with glycogen, lubrication with hyaluronic acid, or cell recognition and oligoproteins.
Hope this help!