The valuation date falls in between coupon payment days on the swap, does the 'price' of a swap understood to include the accrued interest (interest from the previous payment date to the valuation date, as a fraction of the number of days in between) on both legs? Or is it only PV (only counting cashflows starting from the upcoming coupon payments) ?
If you value an existing IRS then you value its official cashflows to their full extent, i.e. implicitly including accrued interest. When an IRS is 'torn up' (or 'bought out' or 'terminated') it is natural to expect discounted value of all of its cashflows.
When a new IRS is 'created' (or 'written' or 'executed') partway through a period it will contain one (or more) 'stub-period'. These are unnatural length periods which settle to an interpolated rate representing the length of the coupon. Since new swaps are rarely created with a backwards start date this is implicitly without accrued interest.