Indeed, and while you design your navy primarily to deliver force to impose your will... whether that is to get you what you need or merely what you are entitled to under international law, it is also about projecting image and brand... and unless your politicians are idiots you should be more propaganda showing the world there is an alternative to my way or the highway western culture... and alternative that wont ram its rules and morals and ideology down your throat and demand you think the way they do.
Let me be clear... the Russian navy is not the worlds policemen and should never be so... that is not their job and shouldn't be their job.
Modular design of their new ships and their upgrades should allow very well armed very well equipped ships be built... having good sensors and the weapons to do something about any situation they come across depends on the size of the vessel... most sensors and weapon launchers are supposed to become more and more multifunctional and over time they will become more so... of course if they have a UKSK launcher and they only ever put anti sub ballistic rockets in it then it is not going to be so flexible in operation, but as long as there is a mix of weapons generally it should be fine... of course the bigger the ship and the more modules fitted and the bigger the sensors fitted the more multi role and comfortable they should be... a Corvette could travel around the world in the sense that you can ride around the country on a motor bike, but unless you work for Top Gear and have ten SUVs full of gear and equipment going with you you will not be super comfortable... unless you stay in 5 star hotels everywhere you stop. It is the US that has bases around the world so that is really only an option for them and selected cronies.
In ten years time when the fleet is bigger and trade ties will be improved with regular visits then agreements with foreign countries about regular use of port areas can be agreed, but right now it probably does not happen often enough to warrant such things except in war zones like Tartus in Syria and Sevastopol.... in Russia