Further to my post Why Scotland should leave the UK and join the EU, Peter Charles points out that some of the items on my list of reserved matters were shared competencies between the UK and EU. He gives this chart:
I thought it might be useful to flesh out a few of these, and see what level of powers independent Scotland would have, versus staying in the UK.
Broadcasting
Scotland would be able to have it's own broadcaster -- like all EU countries do. Yes it would have to obey EU rules.
Immigration and nationality
Scotland would be able to decide who is a Scottish citizen.
It would have to let EU citizens from other EU countries live here. This is what was in effect before January 2020, without causing any big problems.
Wireless telegraphy
EU has common rules on mobile frequencies. This is a good thing as are technical standards in general.
Aerial navigation
The European Common Aviation Area (ECAA) and Eurocontrol aren't actually EU bodies -- though most of their members are in the EU. The UK is in both, even though it has left the EU. Combining air traffic control arrangements through busy airspace is obviously sensible.
Currency
The countries that use the Euro are subject to arrangements on it. Scotland wouldn't be in the Euro, at least at first. It might join later.
Financial services etc
The EU has significant control over these.
Extradition
There is a European Arrest Warrant. Note that even so, it is not automatic that people in one EU member state are extradited to another -- ther state that would receive them has to demonstrate that the accusation against them is of something illegal in the extraditing state and that they would get a fair trial. This is what Julian Assange had court hearings in the UK when Sweden accused him of sexual assault:
On 20 November 2010, the Swedish police issued an international arrest warrant. On 8 December 2010, Assange gave himself up to British police and attended his first extradition hearing where he was remanded in custody. On 16 December 2010, at the second hearing, he was granted bail by the High Court and released after his supporters paid £240,000 in cash and sureties. A further hearing on 24 February 2011 ruled that Assange should be extradited to Sweden. This decision was upheld by the High Court on 2 November and by the Supreme Court on 30 May the next year.
So Scotland would still have significant leeway to not extradite people in politically sensitive cases.
Conclusion
Would independent Scotland, if joining the EU, have to give up some of its independence?
Yes it would, but I don't think the EU's rules are too onerous. The EU isn't a perfect organisation by any means but it does satisfy Scotland's requirement to be part of a larger entity, and does so far better than the UK does (because the EU is bigger than the UK). No other organisation does, so really the EU is the only game in town.