If you were renovating a lawn, spreading compost and/or topsoil might be useful if the soil needs more organic matter, since it can be worked-in to the soil surface to support seedling germination (or rooting-in if you lay sod instead). On the other hand, if you were going to keep augmenting the existing grass instead of replacing it, you can't add much compost/topsoil atop the existing turf without (a) potentially smothering its roots, (b) having some of it erode before the seedlings establish, and (c) potentially conflict with Maryland's lawn fertilizer law, since technically there is a nutrient content to compost that should be accounted-for when tallying the total nitrogen or phosphorus application to a lawn in any given year.

Core-aerating just before seeding is a good step, as it helps to alleviate compaction while increasing the seed-to-soil contact that greatly boosts germination rates. The holes created by aerating would also give a light topdressing of compost/topsoil someplace to settle so less is at risk of eroding.

Has a laboratory soil test been performed? If not, that is the best first step, so the characteristics of organic matter content, nutrient levels, and acidity (pH) can be assessed. Someone (even an experienced lawn company) can't really say with certainty what the soil nutrient profile is like without lab testing. Sometimes root health or soil acidity level is the reason behind a plant having nutrient deficiency symptoms in foliage, rather than deficient soil itself. Insufficient plant vigor is also not always tied to nutrient availability.

We can help to interpret test results if desired, and the lab will provide recommendations for a liming rate if raising the pH would benefit the turf. To curb runoff pollution that harms our watershed, Maryland restricts the use of phosphorus [P] fertilizer on lawns when soil test results do not show a deficiency, so testing also will let you know if you can apply a fertilizer with some P or whether it should be a zero-P formulation. Nitrogen [N] can help green-up a lawn, at least for a while, but there are limits on N applications as well, and lawns fertilized twice in autumn usually don't need another dose in spring unless they are struggling. (That said, the reason for that struggling should be determine first, since a soil test might show that soil levels are plentiful for most key nutrients.)

If the lawn's organic matter content is low, that might be one reason the turf is struggling and certain weeds are faring well. Organic matter helps retain moisture and nutrients, plus resists soil compaction that can stress or kill roots and interfere with good drainage. Adding organic matter passively over time is easily done by using a mulching mower (if you aren't already), which returns finely-chopped grass clippings to the soil surface to decompose. Compost can be a soil additive if the levels are low and you are redoing parts of the lawn, since it can be incorporated at that step.

Mowing height can be one factor behind turf vigor and weed spread, since mowing too low can allow some weed species to thrive while it stresses the turf. By letting the grass get relatively high (near 4 inches) between mows, it can shade-out many weed seeds so they don't become a problem. Some weeds thrive in certain conditions, like too dry, too infertile, or too wet/compacted, so the types of weeds present might indicate a particular issue that can be addressed. The linked page lists all of the common lawn weeds in Maryland, but you are welcome to share photos here for ID if you're not certain what you're seeing.

When possible, lawn renovation or overseeding for cool-season turf should take place in late summer through early autumn, not in spring. There are too many potential complications in spring that make the process more difficult and less likely to be successful. Seeding patching areas prone to erosion is certainly doable now, but other than a renovation that lays sod instead of seed (more costly at first, but also essentially weed-free to start), it's probably best to wait.

Has it been confirmed that thatch is present? Tall fescue lawns, which is what most of Maryland grows for turf that isn't zoysia (one of the only warm-season grasses grown here), does not really develop much thatch like Kentucky bluegrass can. If it's needed, you can dethatch in spring or fall, as long as the turf is in active growth so it can recover faster.

Pre-emergent needs to be chosen based on the weeds needing control. Winter annuals (chickweed, speedwell, cress, etc.), for example, germinate in autumn, so a treatment would need to be put down just before they sprout. Summer annuals are germinating now (or will be soon, since they don't all start at the same time), so a pre-emergent is either slightly too late or could be applied soon. Perennial weeds can of course germinate from seed as well, but once up, they won't respond to a pre-emergent and instead would require a post-emergent to spot-treat them. Systemic herbicides in that case would be the most effective choice since they kill roots so the entire plant dies. Some of those systemics will kill anything the application contacts, while others are a bit more selective.

Any herbicide should have its label read thoroughly before use, and there are many formulations with different groups of weeds controlled (some of which leave grasses unharmed and some of which don't). In some situations, you will not be able to apply a pre-emergent during the same season as you intend to sow grass seed (this depends on the herbicide active ingredients), so you may have to decide which step is more important at that point. Improving the vigor and density of the lawn by overseeding with recommended turf cultivars each year goes a long way to a lawn being able to resist most weed invasion by itself.

Miri