What observation rights are the presidential campaigns (or the parties, or the public) afforded during the counting process - throughout the US and in Pennsylvania specifically?
I think those would be 25 P.S. § 2650 and 25 P.S. § 3146.8. Since the first law is quite succinct, I'll simply quote it:
(a) Any party or political body or body of citizens which now is, or hereafter may be, entitled to have watchers at any registration, primary or election, shall also be entitled to appoint watchers who are qualified electors of the county or attorneys to represent such party or political body or body of citizens at any public session or sessions of the county board of elections, and at any computation and canvassing of returns of any primary or election and recount of ballots or recanvass of voting machines under the provisions of this act. Such watchers or attorneys may exercise the same rights as watchers at registration and polling places, but the number who may be present at any one time may be limited by the county board to not more than three for each party, political body or body of citizens.
(b) Every candidate shall be entitled to be present in person or by attorney in fact duly authorized, and to participate in any proceeding before any county board whenever any matters which may affect his candidacy are being heard, including any computation and canvassing of returns of any primary or election or recount of ballots or recanvass of voting machines affecting his candidacy.
(c) Any candidate, attorney or watcher present at any recount of ballots or recanvass of voting machines shall be entitled to examine the ballots, or the voting machine and to raise any objections regarding the same, which shall be decided by the county board, subject to appeal, in the manner provided by this act.
The second deals with Canvassing of official absentee ballots. Since it's a lot more extensive, I will not quote it here and refer to the page on findlaw.com.
And, given current information, to what extent, if at all, has the Trump campaign been denied exercising these rights in Philadelphia?
NBC Philadelphia reports at least seven lawsuits in Pennsylvania regarding the counting of election results. Two of those seem relevant to me with respect to observation of the count (quote from NBC Philadelphia, links in quote added by me):
In Re: Canvassing Observation
Filed in: Commonwealth Court
Issue: An appeals court ordered Philadelphia to make it easier for observers to watch ballot handing on Thursday, a victory for the Trump campaign. Philadelphia's ballot count was briefly halted as a result. In the meantime, Philadelphia asked the state Supreme Court to grant an appeal, and the city resumed the count.
Status: Acceptance for appeal pending.
and
Trump for President v Philadelphia County Board of Elections
Filed in: Federal court in the Eastern District of Pennsylvania
Issue: Seeks an emergency injunction to stop the vote count in Philadelphia until Republican observers are allowed better access to the canvassing tables. This is similar to one the campaign made Commonwealth Court that briefly halted the count Thursday morning.
Status: The two parties agreed to an accommodation like that in the similar Commonwealth Court case, with both the Trump and Biden campaigns entitled to 60 observers to watch the count.
To answer your question about being denied rights, it's hard to answer that with a value judgement. For example, in In Re: Canvassing Observation the plaintiff was awarded permission to "observe all aspects of the canvassing process within 6 feet, while adhering to all COVID-19 protocols, including, wearing masks and maintaining social distancing." That's a win, but as noted by Westlaw:
Poll observers were allowed before the ruling but had to maintain a greater distance from the ballot canvassing process.
So it's hard to say to what extent anyone was denied exercising their right to observe in this case.
